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class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_tl.wikipedia.org&uselang=tl" class=""><span>Donasyon</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Natatangi:Likhain_ang_kuwenta&returnto=Heometriyang+deribatibo" title="Mas maganda kung gagawa ka ng account at magla-login; gayunpaman, hindi ka pinipilit gawin ito" class=""><span>Gumawa ng account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item 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class="mw-list-item"><a href="/wiki/Natatangi:Usapan_ko" title="Usapang tungkol sa mga pagbabagong ginawa sa ip address na ito [n]" accesskey="n"><span>Usapan</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sayt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Mga nilalaman" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Mga nilalaman</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">ilipat sa gilid</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">itago</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Simula</div> </a> </li> <li id="toc-Mga_sangay" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mga_sangay"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Mga sangay</span> </div> </a> <button aria-controls="toc-Mga_sangay-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Ipakita/Itago ang subseksyon na Mga sangay</span> </button> <ul id="toc-Mga_sangay-sublist" class="vector-toc-list"> <li id="toc-Heometriyang_Riemannian" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriyang_Riemannian"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Heometriyang Riemannian</span> </div> </a> <ul id="toc-Heometriyang_Riemannian-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Heometriyang_Pseudo-Riemannian" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Heometriyang_Pseudo-Riemannian"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Heometriyang Pseudo-Riemannian</span> </div> </a> <button aria-controls="toc-Heometriyang_Pseudo-Riemannian-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Ipakita/Itago ang subseksyon na Heometriyang Pseudo-Riemannian</span> </button> <ul id="toc-Heometriyang_Pseudo-Riemannian-sublist" class="vector-toc-list"> <li id="toc-Heometriyang_Finsler" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriyang_Finsler"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Heometriyang Finsler</span> </div> </a> <ul id="toc-Heometriyang_Finsler-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Heometriyang_Simplektiko" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriyang_Simplektiko"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Heometriyang Simplektiko</span> </div> </a> <ul id="toc-Heometriyang_Simplektiko-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Heometriyang_kontakt" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriyang_kontakt"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Heometriyang kontakt</span> </div> </a> <ul id="toc-Heometriyang_kontakt-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Heometriyang_kompleks_at_Kähler" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriyang_kompleks_at_Kähler"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Heometriyang kompleks at Kähler</span> </div> </a> <ul id="toc-Heometriyang_kompleks_at_Kähler-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Heometriyang_CR" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriyang_CR"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Heometriyang CR</span> </div> </a> <ul id="toc-Heometriyang_CR-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Topolohiyang_diperensiyal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Topolohiyang_diperensiyal"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Topolohiyang diperensiyal</span> </div> </a> <ul id="toc-Topolohiyang_diperensiyal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mga_grupong_Lie" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mga_grupong_Lie"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Mga grupong Lie</span> </div> </a> <ul id="toc-Mga_grupong_Lie-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Mga nilalaman" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Itago/Ipakita ang talaan ng mga nilalaman" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Itago/Ipakita ang talaan ng mga nilalaman</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Heometriyang deribatibo</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Pumunta sa isang artikulo na nakasulat sa ibang wika. Mayroon ito sa 54 (na) wika" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-54" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">54 (na) wika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%87%D9%86%D8%AF%D8%B3%D8%A9_%D8%AA%D9%81%D8%A7%D8%B6%D9%84%D9%8A%D8%A9" title="هندسة تفاضلية – Arabic" lang="ar" hreflang="ar" data-title="هندسة تفاضلية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Xeometr%C3%ADa_diferencial" title="Xeometría diferencial – Asturian" lang="ast" hreflang="ast" data-title="Xeometría diferencial" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D1%8B%D1%84%D0%B5%D1%80%D1%8D%D0%BD%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Дыферэнцыяльная геаметрыя – Belarusian" lang="be" hreflang="be" data-title="Дыферэнцыяльная геаметрыя" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Диференциална геометрия – Bulgarian" lang="bg" hreflang="bg" data-title="Диференциална геометрия" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%8D%E0%A6%AF%E0%A6%AC%E0%A6%95%E0%A6%B2%E0%A6%A8%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%9C%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AE%E0%A6%BF%E0%A6%A4%E0%A6%BF" title="ব্যবকলনীয় জ্যামিতি – Bangla" lang="bn" hreflang="bn" data-title="ব্যবকলনীয় জ্যামিতি" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Geometria_diferencial" title="Geometria diferencial – Catalan" lang="ca" hreflang="ca" data-title="Geometria diferencial" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Diferenci%C3%A1ln%C3%AD_geometrie" title="Diferenciální geometrie – Czech" lang="cs" hreflang="cs" data-title="Diferenciální geometrie" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%BB%C4%83_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8" title="Дифференциаллă геометри – Chuvash" lang="cv" hreflang="cv" data-title="Дифференциаллă геометри" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Differentialgeometri" title="Differentialgeometri – Danish" lang="da" hreflang="da" data-title="Differentialgeometri" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Differentialgeometrie" title="Differentialgeometrie – German" lang="de" hreflang="de" data-title="Differentialgeometrie" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CE%B1%CF%86%CE%BF%CF%81%CE%B9%CE%BA%CE%AE_%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1" title="Διαφορική γεωμετρία – Greek" lang="el" hreflang="el" data-title="Διαφορική γεωμετρία" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Differential_geometry" title="Differential geometry – English" lang="en" hreflang="en" data-title="Differential geometry" data-language-autonym="English" data-language-local-name="English" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Diferenciala_geometrio" title="Diferenciala geometrio – Esperanto" lang="eo" hreflang="eo" data-title="Diferenciala geometrio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Geometr%C3%ADa_diferencial" title="Geometría diferencial – Spanish" lang="es" hreflang="es" data-title="Geometría diferencial" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Diferentsiaalgeomeetria" title="Diferentsiaalgeomeetria – Estonian" lang="et" hreflang="et" data-title="Diferentsiaalgeomeetria" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Geometria_diferentzial" title="Geometria diferentzial – Basque" lang="eu" hreflang="eu" data-title="Geometria diferentzial" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%87%D9%86%D8%AF%D8%B3%D9%87_%D8%AF%DB%8C%D9%81%D8%B1%D8%A7%D9%86%D8%B3%DB%8C%D9%84" title="هندسه دیفرانسیل – Persian" lang="fa" hreflang="fa" data-title="هندسه دیفرانسیل" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Differentiaaligeometria" title="Differentiaaligeometria – Finnish" lang="fi" hreflang="fi" data-title="Differentiaaligeometria" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/G%C3%A9om%C3%A9trie_diff%C3%A9rentielle" title="Géométrie différentielle – French" lang="fr" hreflang="fr" data-title="Géométrie différentielle" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Xeometr%C3%ADa_diferencial" title="Xeometría diferencial – Galician" lang="gl" hreflang="gl" data-title="Xeometría diferencial" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94_%D7%93%D7%99%D7%A4%D7%A8%D7%A0%D7%A6%D7%99%D7%90%D7%9C%D7%99%D7%AA" title="גאומטריה דיפרנציאלית – Hebrew" lang="he" hreflang="he" data-title="גאומטריה דיפרנציאלית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%B5%E0%A4%95%E0%A4%B2_%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF" title="अवकल ज्यामिति – Hindi" lang="hi" hreflang="hi" data-title="अवकल ज्यामिति" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Diferencijalna_geometrija" title="Diferencijalna geometrija – Croatian" lang="hr" hreflang="hr" data-title="Diferencijalna geometrija" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Differenci%C3%A1lgeometria" title="Differenciálgeometria – Hungarian" lang="hu" hreflang="hu" data-title="Differenciálgeometria" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B4%D5%AB%D6%86%D5%A5%D6%80%D5%A5%D5%B6%D6%81%D5%AB%D5%A1%D5%AC_%D5%A5%D6%80%D5%AF%D6%80%D5%A1%D5%B9%D5%A1%D6%83%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Դիֆերենցիալ երկրաչափություն – Armenian" lang="hy" hreflang="hy" data-title="Դիֆերենցիալ երկրաչափություն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Geometri_diferensial" title="Geometri diferensial – Indonesian" lang="id" hreflang="id" data-title="Geometri diferensial" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Geometria_differenziale" title="Geometria differenziale – Italian" lang="it" hreflang="it" data-title="Geometria differenziale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%BE%AE%E5%88%86%E5%B9%BE%E4%BD%95%E5%AD%A6" title="微分幾何学 – Japanese" lang="ja" hreflang="ja" data-title="微分幾何学" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%93%E1%83%98%E1%83%A4%E1%83%94%E1%83%A0%E1%83%94%E1%83%9C%E1%83%AA%E1%83%98%E1%83%90%E1%83%9A%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%92%E1%83%94%E1%83%9D%E1%83%9B%E1%83%94%E1%83%A2%E1%83%A0%E1%83%98%E1%83%90_%E1%83%93%E1%83%90_%E1%83%A2%E1%83%9D%E1%83%9E%E1%83%9D%E1%83%9A%E1%83%9D%E1%83%92%E1%83%98%E1%83%90" title="დიფერენციალური გეომეტრია და ტოპოლოგია – Georgian" lang="ka" hreflang="ka" data-title="დიფერენციალური გეომეტრია და ტოპოლოგია" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AF%B8%EB%B6%84%EA%B8%B0%ED%95%98%ED%95%99" title="미분기하학 – Korean" lang="ko" hreflang="ko" data-title="미분기하학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Diferencialin%C4%97_geometrija" title="Diferencialinė geometrija – Lithuanian" lang="lt" hreflang="lt" data-title="Diferencialinė geometrija" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Geometri_pembezaan" title="Geometri pembezaan – Malay" lang="ms" hreflang="ms" data-title="Geometri pembezaan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%92%E1%80%85%E1%80%BA%E1%80%96%E1%80%9B%E1%80%94%E1%80%BA%E1%80%9B%E1%80%BE%E1%80%9A%E1%80%BA%E1%80%82%E1%80%BB%E1%80%AE%E1%80%A9%E1%80%99%E1%80%B1%E1%80%90%E1%80%BC%E1%80%AE" title="ဒစ်ဖရန်ရှယ်ဂျီဩမေတြီ – Burmese" lang="my" hreflang="my" data-title="ဒစ်ဖရန်ရှယ်ဂျီဩမေတြီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Differentiaalmeetkunde" title="Differentiaalmeetkunde – Dutch" lang="nl" hreflang="nl" data-title="Differentiaalmeetkunde" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Differensialgeometri" title="Differensialgeometri – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Differensialgeometri" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Differensialgeometri" title="Differensialgeometri – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Differensialgeometri" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Geometria_r%C3%B3%C5%BCniczkowa" title="Geometria różniczkowa – Polish" lang="pl" hreflang="pl" data-title="Geometria różniczkowa" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Geometria_diferencial" title="Geometria diferencial – Portuguese" lang="pt" hreflang="pt" data-title="Geometria diferencial" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Geometrie_diferen%C8%9Bial%C4%83" title="Geometrie diferențială – Romanian" lang="ro" hreflang="ro" data-title="Geometrie diferențială" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Дифференциальная геометрия – Russian" lang="ru" hreflang="ru" data-title="Дифференциальная геометрия" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Diferencijalna_geometrija" title="Diferencijalna geometrija – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Diferencijalna geometrija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Differential_geometry" title="Differential geometry – Simple English" lang="en-simple" hreflang="en-simple" data-title="Differential geometry" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Diferenci%C3%A1lna_geometria" title="Diferenciálna geometria – Slovak" lang="sk" hreflang="sk" data-title="Diferenciálna geometria" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Gjeometria_diferenciale" title="Gjeometria diferenciale – Albanian" lang="sq" hreflang="sq" data-title="Gjeometria diferenciale" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Diferencijalna_geometrija" title="Diferencijalna geometrija – Serbian" lang="sr" hreflang="sr" data-title="Diferencijalna geometrija" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Differentialgeometri" title="Differentialgeometri – Swedish" lang="sv" hreflang="sv" data-title="Differentialgeometri" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D2%B2%D0%B0%D0%BD%D0%B4%D0%B0%D1%81%D0%B0%D0%B8_%D0%B4%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%81%D0%B8%D0%B0%D0%BB" title="Ҳандасаи дифференсиал – Tajik" lang="tg" hreflang="tg" data-title="Ҳандасаи дифференсиал" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Diferansiyel_geometri" title="Diferansiyel geometri – Turkish" lang="tr" hreflang="tr" data-title="Diferansiyel geometri" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D1%96%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F" title="Диференціальна геометрія – Ukrainian" lang="uk" hreflang="uk" data-title="Диференціальна геометрія" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Differensial_geometriya" title="Differensial geometriya – Uzbek" lang="uz" hreflang="uz" data-title="Differensial geometriya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%ACnh_h%E1%BB%8Dc_vi_ph%C3%A2n" title="Hình học vi phân – Vietnamese" lang="vi" hreflang="vi" data-title="Hình học vi phân" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%BE%AE%E5%88%86%E5%87%A0%E4%BD%95" title="微分几何 – Wu" lang="wuu" hreflang="wuu" data-title="微分几何" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%BE%AE%E5%88%86%E5%87%A0%E4%BD%95" title="微分几何 – Chinese" lang="zh" hreflang="zh" data-title="微分几何" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a 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</div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="tl" dir="ltr"><table class="vertical-navbox nowraplinks plainlist" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;background:white;"><tbody><tr><th style="padding:0.2em 0.4em 0.2em;font-size:145%;line-height:1.2em"><a href="/wiki/Heometriya" title="Heometriya">Heometriya</a></th></tr><tr><td style="padding:0.2em 0 0.4em"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/Talaksan:Stereographic_projection_in_3D.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Stereographic_projection_in_3D.svg/220px-Stereographic_projection_in_3D.svg.png" decoding="async" width="220" height="162" class="mw-file-element" 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0 0.4em;text-align:center"> <ul><li><a href="/w/index.php?title=Euclidean_geometry&action=edit&redlink=1" class="new" title="Euclidean geometry (hindi pa naisusulat)">Euclidean</a></li> <li><a href="/w/index.php?title=Non-Euclidean_geometry&action=edit&redlink=1" class="new" title="Non-Euclidean geometry (hindi pa naisusulat)">Non-Euclidean</a> <ul><li><a href="/w/index.php?title=Elliptic_geometry&action=edit&redlink=1" class="new" title="Elliptic geometry (hindi pa naisusulat)">Elliptic</a> <ul><li><a href="/w/index.php?title=Spherical_geometry&action=edit&redlink=1" class="new" title="Spherical geometry (hindi pa naisusulat)">Spherical</a></li></ul></li> <li><a href="/w/index.php?title=Hyperbolic_geometry&action=edit&redlink=1" class="new" title="Hyperbolic geometry (hindi pa naisusulat)">Hyperbolic</a></li></ul></li> <li><a href="/w/index.php?title=Non-Archimedean_geometry&action=edit&redlink=1" class="new" title="Non-Archimedean geometry (hindi pa naisusulat)">Non-Archimedean geometry</a></li> <li><a href="/w/index.php?title=Projective_geometry&action=edit&redlink=1" class="new" title="Projective geometry (hindi pa naisusulat)">Projective</a></li> <li><a href="/w/index.php?title=Affine_geometry&action=edit&redlink=1" class="new" title="Affine geometry (hindi pa naisusulat)">Affine</a></li> <li><a href="/w/index.php?title=Synthetic_geometry&action=edit&redlink=1" class="new" title="Synthetic geometry (hindi pa naisusulat)">Synthetic</a></li> <li><a href="/wiki/Analitikong_heometriya" class="mw-redirect" title="Analitikong heometriya">Analitiko</a></li> <li><a href="/wiki/Alhebraikong_heometriya" class="mw-redirect" title="Alhebraikong heometriya">Alhebraiko</a> <ul><li><a href="/w/index.php?title=Arithmetic_geometry&action=edit&redlink=1" class="new" title="Arithmetic geometry (hindi pa naisusulat)">Arithmetic</a></li> <li><a href="/w/index.php?title=Diophantine_geometry&action=edit&redlink=1" class="new" title="Diophantine geometry (hindi pa naisusulat)">Diophantine</a></li></ul></li> <li><a class="mw-selflink selflink">Deribatibo</a> <ul><li><a href="/wiki/Heometriyang_Riemanniano" title="Heometriyang Riemanniano">Riemanniano</a></li> <li><a href="/w/index.php?title=Symplectic_geometry&action=edit&redlink=1" class="new" title="Symplectic geometry (hindi pa naisusulat)">Symplectic</a></li> <li><a href="/w/index.php?title=Discrete_differential_geometry&action=edit&redlink=1" class="new" title="Discrete differential geometry (hindi pa naisusulat)">Discrete differential</a></li></ul></li> <li><a href="/w/index.php?title=Complex_geometry&action=edit&redlink=1" class="new" title="Complex geometry (hindi pa naisusulat)">Complex</a></li> <li><a href="/w/index.php?title=Finite_geometry&action=edit&redlink=1" class="new" title="Finite geometry (hindi pa naisusulat)">Finite</a></li> <li><a href="/wiki/Heometriyang_natatangi" title="Heometriyang natatangi">Natatangi</a> <ul><li><a href="/w/index.php?title=Digital_geometry&action=edit&redlink=1" class="new" title="Digital geometry (hindi pa naisusulat)">Digital</a></li></ul></li> <li><a href="/w/index.php?title=Convex_geometry&action=edit&redlink=1" class="new" title="Convex geometry (hindi pa naisusulat)">Convex</a></li> <li><a href="/w/index.php?title=Computational_geometry&action=edit&redlink=1" class="new" title="Computational geometry (hindi pa naisusulat)">Computational</a></li> <li><a href="/w/index.php?title=Fractal&action=edit&redlink=1" class="new" title="Fractal (hindi pa naisusulat)">Fractal</a></li> <li><a href="/w/index.php?title=Incidence_geometry&action=edit&redlink=1" class="new" title="Incidence geometry (hindi pa naisusulat)">Incidence </a></li> <li><a href="/w/index.php?title=Noncommutative_geometry&action=edit&redlink=1" class="new" title="Noncommutative geometry (hindi pa naisusulat)">Noncommutative geometry</a> <ul><li><a href="/w/index.php?title=Noncommutative_algebraic_geometry&action=edit&redlink=1" class="new" title="Noncommutative algebraic geometry (hindi pa naisusulat)">Noncommutative algebraic geometry</a></li></ul></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;"><div class="hlist hlist-separated"><ul><li>Mga konsepto</li><li>Mga katangian</li></ul></div></div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><a href="/wiki/Dimensiyon" title="Dimensiyon">Dimensiyon</a> <ul><li><a href="/w/index.php?title=Straightedge_and_compass_construction&action=edit&redlink=1" class="new" title="Straightedge and compass construction (hindi pa naisusulat)">Straightedge and compass constructions</a></li></ul> <ul><li><a href="/wiki/Anggulo" title="Anggulo">Anggulo</a></li> <li><a href="/wiki/Kurba" title="Kurba">Kurba</a></li> <li><a href="/w/index.php?title=Diagonal&action=edit&redlink=1" class="new" title="Diagonal (hindi pa naisusulat)">Diagonal</a></li> <li><a href="/wiki/Ortogonalidad" title="Ortogonalidad">Ortogonalidad</a> (<a href="/wiki/Perpendikular" title="Perpendikular">Perpendikular</a>)</li> <li><a href="/wiki/Paralelo" title="Paralelo">Paralelo</a></li> <li><a href="/w/index.php?title=Vertex_(geometry)&action=edit&redlink=1" class="new" title="Vertex (geometry) (hindi pa naisusulat)">Vertex</a></li></ul> <ul><li><a href="/w/index.php?title=Congruence_(geometry)&action=edit&redlink=1" class="new" title="Congruence (geometry) (hindi pa naisusulat)">Congruence</a></li> <li><a href="/w/index.php?title=Similarity_(geometry)&action=edit&redlink=1" class="new" title="Similarity (geometry) (hindi pa naisusulat)">Similarity</a></li> <li><a href="/wiki/Symmetry" class="mw-redirect" title="Symmetry">Symmetry</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;"><a href="/w/index.php?title=Serong_dimensiyonal_na_espasyo&action=edit&redlink=1" class="new" title="Serong dimensiyonal na espasyo (hindi pa naisusulat)">Serong dimensiyonal</a></div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/wiki/Punto_(heometriya)" title="Punto (heometriya)">Punto</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;"><a href="/w/index.php?title=Isang_dimensiyonal_na_espasyo&action=edit&redlink=1" class="new" title="Isang dimensiyonal na espasyo (hindi pa naisusulat)">Isang dimensiyonal</a></div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/wiki/Guhit_(heometriya)" title="Guhit (heometriya)">Guhit</a> <ul><li><a href="/wiki/Linyang_segmento" title="Linyang segmento">Segmento</a></li> <li><a href="/wiki/Guhit_(heometriya)#Rayos" title="Guhit (heometriya)">Rayos</a></li></ul></li> <li><a href="/wiki/Haba" title="Haba">Haba</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;"><a href="/w/index.php?title=Dalawang_dimensiyonal_na_espasyo&action=edit&redlink=1" class="new" title="Dalawang dimensiyonal na espasyo (hindi pa naisusulat)">Dalawang dimensiyonal</a></div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center;padding-bottom:0;"><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;background-color: transparent; border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/Plano_(heometriya)" title="Plano (heometriya)">Plano</a></li> <li><a href="/wiki/Sukat" title="Sukat">Sukat</a></li> <li><a href="/wiki/Poligon" title="Poligon">Poligon</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> <a href="/wiki/Tatsulok" title="Tatsulok">Tatsulok</a></th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/w/index.php?title=Altitude_(triangle)&action=edit&redlink=1" class="new" title="Altitude (triangle) (hindi pa naisusulat)">Altitude</a></li> <li><a href="/wiki/Gilis" class="mw-redirect" title="Gilis">Gilis</a></li> <li><a href="/wiki/Teorema_ni_Pitagoras" title="Teorema ni Pitagoras">Teorema ni Pitagoras</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> <a href="/wiki/Paralelogram" title="Paralelogram">Paralelogram</a></th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/Parisukat" title="Parisukat">Parisukat</a></li> <li><a href="/wiki/Parihaba" title="Parihaba">Parihaba</a></li> <li><a href="/wiki/Rombus" title="Rombus">Rombus</a></li> <li><a href="/w/index.php?title=Romboide&action=edit&redlink=1" class="new" title="Romboide (hindi pa naisusulat)">Romboide</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> <a href="/wiki/Kuwadrilateral" title="Kuwadrilateral">Kuwadrilateral</a></th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/Trapesoid" title="Trapesoid">Trapesoid</a></li> <li><a href="/w/index.php?title=Kite_(geometry)&action=edit&redlink=1" class="new" title="Kite (geometry) (hindi pa naisusulat)">Kite</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> <a href="/wiki/Bilog" title="Bilog">Bilog</a></th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/Diyametro" title="Diyametro">Diyametro</a></li> <li><a href="/wiki/Sirkumperensiya" title="Sirkumperensiya">Sirkumperensiya</a></li> <li><a href="/w/index.php?title=Area_of_a_circle&action=edit&redlink=1" class="new" title="Area of a circle (hindi pa naisusulat)">Area</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;"><a href="/wiki/Tatlong_dimensiyonal_na_espasyo" class="mw-redirect" title="Tatlong dimensiyonal na espasyo">Tatlong dimensiyonal</a></div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/wiki/Volyum" title="Volyum">Volyum</a></li></ul> <ul><li><a href="/w/index.php?title=Kubo_(hugis)&action=edit&redlink=1" class="new" title="Kubo (hugis) (hindi pa naisusulat)">Kubo</a> <ul><li><a href="/w/index.php?title=Kuboide&action=edit&redlink=1" class="new" title="Kuboide (hindi pa naisusulat)">Kuboide</a></li></ul></li> <li><a href="/w/index.php?title=Silindro_(hugis)&action=edit&redlink=1" class="new" title="Silindro (hugis) (hindi pa naisusulat)">Silindro</a></li> <li><a href="/w/index.php?title=Dodecahedron&action=edit&redlink=1" class="new" title="Dodecahedron (hindi pa naisusulat)">Dodecahedron</a></li> <li><a href="/w/index.php?title=Icosahedron&action=edit&redlink=1" class="new" title="Icosahedron (hindi pa naisusulat)">Icosahedron</a></li> <li><a href="/w/index.php?title=Octahedron&action=edit&redlink=1" class="new" title="Octahedron (hindi pa naisusulat)">Octahedron</a></li> <li><a href="/w/index.php?title=Piramide_(hugis)&action=edit&redlink=1" class="new" title="Piramide (hugis) (hindi pa naisusulat)">Piramide</a></li> <li><a href="/w/index.php?title=Platonic_Solid&action=edit&redlink=1" class="new" title="Platonic Solid (hindi pa naisusulat)">Platonic Solid</a></li> <li><a href="/w/index.php?title=Sphere&action=edit&redlink=1" class="new" title="Sphere (hindi pa naisusulat)">Sphere</a></li> <li><a href="/w/index.php?title=Tetrahedron&action=edit&redlink=1" class="new" title="Tetrahedron (hindi pa naisusulat)">Tetrahedron</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;"><a href="/w/index.php?title=Apat_na_dimensiyonal_na_espasyo&action=edit&redlink=1" class="new" title="Apat na dimensiyonal na espasyo (hindi pa naisusulat)">Apat</a>- / ibang-dimensiyonal</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/w/index.php?title=Tesseract&action=edit&redlink=1" class="new" title="Tesseract (hindi pa naisusulat)">Tesseract</a></li> <li><a href="/w/index.php?title=Hypersphere&action=edit&redlink=1" class="new" title="Hypersphere (hindi pa naisusulat)">Hypersphere</a></li></ul></div></div></td> </tr><tr><th style="padding:0.1em;padding-bottom:0.2em;"> Mga heometra</th></tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;">ayon sa pangalan</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/w/index.php?title=Yasuaki_Aida&action=edit&redlink=1" class="new" title="Yasuaki Aida (hindi pa naisusulat)">Aida</a></li> <li><a href="/w/index.php?title=Aryabhata&action=edit&redlink=1" class="new" title="Aryabhata (hindi pa naisusulat)">Aryabhata</a></li> <li><a href="/w/index.php?title=Ahmes&action=edit&redlink=1" class="new" title="Ahmes (hindi pa naisusulat)">Ahmes</a></li> <li><a href="/w/index.php?title=Alhazen&action=edit&redlink=1" class="new" title="Alhazen (hindi pa naisusulat)">Alhazen</a></li> <li><a href="/w/index.php?title=Apollonius_of_Perga&action=edit&redlink=1" class="new" title="Apollonius of Perga (hindi pa naisusulat)">Apollonius</a></li> <li><a href="/wiki/Arkimedes" title="Arkimedes">Arkimedes</a></li> <li><a href="/w/index.php?title=Michael_Atiyah&action=edit&redlink=1" class="new" title="Michael Atiyah (hindi pa naisusulat)">Atiyah</a></li> <li><a href="/w/index.php?title=Baudhayana&action=edit&redlink=1" class="new" title="Baudhayana (hindi pa naisusulat)">Baudhayana</a></li> <li><a href="/w/index.php?title=J%C3%A1nos_Bolyai&action=edit&redlink=1" class="new" title="János Bolyai (hindi pa naisusulat)">Bolyai</a></li> <li><a href="/wiki/Brahmagupta" title="Brahmagupta">Brahmagupta</a></li> <li><a href="/w/index.php?title=%C3%89lie_Cartan&action=edit&redlink=1" class="new" title="Élie Cartan (hindi pa naisusulat)">Cartan</a></li> <li><a href="/w/index.php?title=Harold_Scott_MacDonald_Coxeter&action=edit&redlink=1" class="new" title="Harold Scott MacDonald Coxeter (hindi pa naisusulat)">Coxeter</a></li> <li><a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">Descartes</a></li> <li><a href="/wiki/Euclides" title="Euclides">Euclides</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a></li> <li><a href="/w/index.php?title=Mikhail_Leonidovich_Gromov&action=edit&redlink=1" class="new" title="Mikhail Leonidovich Gromov (hindi pa naisusulat)">Gromov</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a></li> <li><a href="/w/index.php?title=Jye%E1%B9%A3%E1%B9%ADhadeva&action=edit&redlink=1" class="new" title="Jyeṣṭhadeva (hindi pa naisusulat)">Jyeṣṭhadeva</a></li> <li><a href="/w/index.php?title=K%C4%81ty%C4%81yana&action=edit&redlink=1" class="new" title="Kātyāyana (hindi pa naisusulat)">Kātyāyana</a></li> <li><a href="/wiki/Omar_Khayy%C3%A1m" class="mw-redirect" title="Omar Khayyám">Khayyám</a></li> <li><a href="/wiki/Felix_Klein" title="Felix Klein">Klein</a></li> <li><a href="/w/index.php?title=Nikolai_Lobachevsky&action=edit&redlink=1" class="new" title="Nikolai Lobachevsky (hindi pa naisusulat)">Lobachevsky</a></li> <li><a href="/w/index.php?title=Manava&action=edit&redlink=1" class="new" title="Manava (hindi pa naisusulat)">Manava</a></li> <li><a href="/w/index.php?title=Hermann_Minkowski&action=edit&redlink=1" class="new" title="Hermann Minkowski (hindi pa naisusulat)">Minkowski</a></li> <li><a href="/w/index.php?title=Minggatu&action=edit&redlink=1" class="new" title="Minggatu (hindi pa naisusulat)">Minggatu</a></li> <li><a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Pascal</a></li> <li><a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a></li> <li><a href="/w/index.php?title=Parameshvara&action=edit&redlink=1" class="new" title="Parameshvara (hindi pa naisusulat)">Parameshvara</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li> <li><a href="/wiki/Bernhard_Riemann" title="Bernhard Riemann">Riemann</a></li> <li><a href="/w/index.php?title=Sakabe_K%C5%8Dhan&action=edit&redlink=1" class="new" title="Sakabe Kōhan (hindi pa naisusulat)">Sakabe</a></li> <li><a href="/w/index.php?title=Sijzi&action=edit&redlink=1" class="new" title="Sijzi (hindi pa naisusulat)">Sijzi</a></li> <li><a href="/w/index.php?title=Nasir_al-Din_al-Tusi&action=edit&redlink=1" class="new" title="Nasir al-Din al-Tusi (hindi pa naisusulat)">al-Tusi</a></li> <li><a href="/w/index.php?title=Oswald_Veblen&action=edit&redlink=1" class="new" title="Oswald Veblen (hindi pa naisusulat)">Veblen</a></li> <li><a href="/w/index.php?title=Virasena&action=edit&redlink=1" class="new" title="Virasena (hindi pa naisusulat)">Virasena</a></li> <li><a href="/w/index.php?title=Yang_Hui&action=edit&redlink=1" class="new" title="Yang Hui (hindi pa naisusulat)">Yang Hui</a></li> <li><a href="/w/index.php?title=Ibn_al-Yasamin&action=edit&redlink=1" class="new" title="Ibn al-Yasamin (hindi pa naisusulat)">al-Yasamin</a></li> <li><a href="/wiki/Zhang_Heng" title="Zhang Heng">Zhang</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;">ayon sa panahon</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center;padding-bottom:0;"><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;background-color: transparent; border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> <a href="/w/index.php?title=Before_Common_Era&action=edit&redlink=1" class="new" title="Before Common Era (hindi pa naisusulat)">BCE</a></th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/w/index.php?title=Ahmes&action=edit&redlink=1" class="new" title="Ahmes (hindi pa naisusulat)">Ahmes</a></li> <li><a href="/w/index.php?title=Baudhayana&action=edit&redlink=1" class="new" title="Baudhayana (hindi pa naisusulat)">Baudhayana</a></li> <li><a href="/w/index.php?title=Manava&action=edit&redlink=1" class="new" title="Manava (hindi pa naisusulat)">Manava</a></li> <li><a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a></li> <li><a href="/wiki/Euclid" class="mw-redirect" title="Euclid">Euclid</a></li> <li><a href="/wiki/Archimedes" class="mw-redirect" title="Archimedes">Archimedes</a></li> <li><a href="/w/index.php?title=Apollonius_of_Perga&action=edit&redlink=1" class="new" title="Apollonius of Perga (hindi pa naisusulat)">Apollonius</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> 1–1400s</th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/Zhang_Heng" title="Zhang Heng">Zhang</a></li> <li><a href="/w/index.php?title=K%C4%81ty%C4%81yana&action=edit&redlink=1" class="new" title="Kātyāyana (hindi pa naisusulat)">Kātyāyana</a></li> <li><a href="/w/index.php?title=Aryabhata&action=edit&redlink=1" class="new" title="Aryabhata (hindi pa naisusulat)">Aryabhata</a></li> <li><a href="/wiki/Brahmagupta" title="Brahmagupta">Brahmagupta</a></li> <li><a href="/w/index.php?title=Virasena&action=edit&redlink=1" class="new" title="Virasena (hindi pa naisusulat)">Virasena</a></li> <li><a href="/w/index.php?title=Alhazen&action=edit&redlink=1" class="new" title="Alhazen (hindi pa naisusulat)">Alhazen</a></li> <li><a href="/w/index.php?title=Sijzi&action=edit&redlink=1" class="new" title="Sijzi (hindi pa naisusulat)">Sijzi</a></li> <li><a href="/wiki/Omar_Khayy%C3%A1m" class="mw-redirect" title="Omar Khayyám">Khayyám</a></li> <li><a href="/w/index.php?title=Ibn_al-Yasamin&action=edit&redlink=1" class="new" title="Ibn al-Yasamin (hindi pa naisusulat)">al-Yasamin</a></li> <li><a href="/w/index.php?title=Nasir_al-Din_al-Tusi&action=edit&redlink=1" class="new" title="Nasir al-Din al-Tusi (hindi pa naisusulat)">al-Tusi</a></li> <li><a href="/w/index.php?title=Yang_Hui&action=edit&redlink=1" class="new" title="Yang Hui (hindi pa naisusulat)">Yang Hui</a></li> <li><a href="/w/index.php?title=Parameshvara&action=edit&redlink=1" class="new" title="Parameshvara (hindi pa naisusulat)">Parameshvara</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> 1400s–1700s</th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/w/index.php?title=Jye%E1%B9%A3%E1%B9%ADhadeva&action=edit&redlink=1" class="new" title="Jyeṣṭhadeva (hindi pa naisusulat)">Jyeṣṭhadeva</a></li> <li><a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">Descartes</a></li> <li><a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Pascal</a></li> <li><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a></li> <li><a href="/w/index.php?title=Minggatu&action=edit&redlink=1" class="new" title="Minggatu (hindi pa naisusulat)">Minggatu</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/w/index.php?title=Sakabe_K%C5%8Dhan&action=edit&redlink=1" class="new" title="Sakabe Kōhan (hindi pa naisusulat)">Sakabe</a></li> <li><a href="/w/index.php?title=Yasuaki_Aida&action=edit&redlink=1" class="new" title="Yasuaki Aida (hindi pa naisusulat)">Aida</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> 1700s–1900s</th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a></li> <li><a href="/w/index.php?title=Nikolai_Lobachevsky&action=edit&redlink=1" class="new" title="Nikolai Lobachevsky (hindi pa naisusulat)">Lobachevsky</a></li> <li><a href="/w/index.php?title=J%C3%A1nos_Bolyai&action=edit&redlink=1" class="new" title="János Bolyai (hindi pa naisusulat)">Bolyai</a></li> <li><a href="/wiki/Bernhard_Riemann" title="Bernhard Riemann">Riemann</a></li> <li><a href="/wiki/Felix_Klein" title="Felix Klein">Klein</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/w/index.php?title=Hermann_Minkowski&action=edit&redlink=1" class="new" title="Hermann Minkowski (hindi pa naisusulat)">Minkowski</a></li> <li><a href="/w/index.php?title=%C3%89lie_Cartan&action=edit&redlink=1" class="new" title="Élie Cartan (hindi pa naisusulat)">Cartan</a></li> <li><a href="/w/index.php?title=Oswald_Veblen&action=edit&redlink=1" class="new" title="Oswald Veblen (hindi pa naisusulat)">Veblen</a></li> <li><a href="/w/index.php?title=Harold_Scott_MacDonald_Coxeter&action=edit&redlink=1" class="new" title="Harold Scott MacDonald Coxeter (hindi pa naisusulat)">Coxeter</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> Present day</th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/w/index.php?title=Michael_Atiyah&action=edit&redlink=1" class="new" title="Michael Atiyah (hindi pa naisusulat)">Atiyah</a></li> <li><a href="/w/index.php?title=Mikhail_Leonidovich_Gromov&action=edit&redlink=1" class="new" title="Mikhail Leonidovich Gromov (hindi pa naisusulat)">Gromov</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td style="text-align:right;font-size:115%;padding-top: 0.6em;"><style data-mw-deduplicate="TemplateStyles:r1843287">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}.mw-parser-output .infobox .navbar{font-size:100%}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-tingnan"><a href="/wiki/Padron:Pangkalahatang_heometriya" title="Padron:Pangkalahatang heometriya"><abbr title="Tingnan ang padron">t</abbr></a></li><li class="nv-usapan"><a href="/w/index.php?title=Usapang_padron:Pangkalahatang_heometriya&action=edit&redlink=1" class="new" title="Usapang padron:Pangkalahatang heometriya (hindi pa naisusulat)"><abbr title="Pag-usapan ang padron">u</abbr></a></li><li class="nv-baguhin"><a class="external text" href="https://tl.wikipedia.org/w/index.php?title=Padron:Pangkalahatang_heometriya&action=edit"><abbr title="Baguhin ang padron">b</abbr></a></li></ul></div></td></tr></tbody></table> <p>Ang <b>diperensiyal na heometriya</b> ay isang disiplina sa <a href="/wiki/Matematika" title="Matematika">matematika</a> na gumagamit ng mga tekniko ng <a href="/wiki/Deribatibo" title="Deribatibo">diperensiyal</a> at <a href="/wiki/Integral" class="mw-redirect" title="Integral">integral</a> na <a href="/wiki/Kalkulo" class="mw-redirect" title="Kalkulo">kalkulo</a> gayundin ang <a href="/wiki/Linear_algebra" class="mw-redirect" title="Linear algebra">linyar</a> at <a href="/wiki/Multilinear_algebra" class="mw-redirect" title="Multilinear algebra">multilinear algebra</a> upang pag-aralan ang mga problema sa <a href="/wiki/Heometriya" title="Heometriya">heometriya</a>. Simula noong huling yugto noong ikalabing siyam na siglo, ang diperensiyal na heometriya ay lumago sa larangang nauukol sa mas heneral na mga heometrikong straktura sa mga <a href="/wiki/Manipoldong_diperensiyable" class="mw-redirect" title="Manipoldong diperensiyable">manipoldong diperensiyable</a>. Ito ay malapit na nauugnay din sa <a href="/wiki/Diperensiyal_na_topolohiya" class="mw-redirect" title="Diperensiyal na topolohiya">diperensiyal na topolohiya</a> at sa mga aspetong heometiko ng ng teoriya ng mga <a href="/wiki/Diperensiyal_na_ekwasyon" class="mw-redirect" title="Diperensiyal na ekwasyon">diperensiyal na ekwasyon</a>. Ang patunay ni <a href="/w/index.php?title=Grigori_Perelman&action=edit&redlink=1" class="new" title="Grigori Perelman (hindi pa naisusulat)">Grigori Perelman</a> ng <a href="/w/index.php?title=Konhekturang_Poincar%C3%A9&action=edit&redlink=1" class="new" title="Konhekturang Poincaré (hindi pa naisusulat)">konhekturang Poincaré</a> gamit ang mga tekniko ng <a href="/wiki/Daloy_Ricci" title="Daloy Ricci">daloy Ricci</a> ay nagpakita ng kapangyarihan ng paraang diperensiyal heometriko sa mga katanungan sa topolohiya at nagbigay diin din ito ng mahalagang papel na ginagampanan sa mga paraang analitiko. Ang <a href="/w/index.php?title=Diperensiyal_na_heometriya_ng_mga_surpasiyo&action=edit&redlink=1" class="new" title="Diperensiyal na heometriya ng mga surpasiyo (hindi pa naisusulat)">diperensiyal na heometriya ng mga surpasiyo</a> ay sumasakop sa maraming mga mahahalagang ideya at tekniko na katangian ng larangang ito. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Mga_sangay">Mga sangay</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriyang_deribatibo&veaction=edit&section=1" title="Baguhin seksiyon: Mga sangay" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriyang_deribatibo&action=edit&section=1" title="Edit section's source code: Mga sangay"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Heometriyang_Riemannian">Heometriyang Riemannian</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriyang_deribatibo&veaction=edit&section=2" title="Baguhin seksiyon: Heometriyang Riemannian" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriyang_deribatibo&action=edit&section=2" title="Edit section's source code: Heometriyang Riemannian"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Pangunahing artikulo: <a href="/wiki/Heometriyang_Riemannian" class="mw-redirect" title="Heometriyang Riemannian">Heometriyang Riemannian</a></div> <p>Ang heometriyang Riemannian ay nag-aaral ng mga <a href="/wiki/Manipoldong_Riemannian" class="mw-redirect" title="Manipoldong Riemannian">manipoldong Riemannian</a>, mga <a href="/wiki/Diperensiyableng_manipoldo" class="mw-redirect" title="Diperensiyableng manipoldo">diperensiyableng manipoldo</a> na inihahayag sa pamamagitan ng makinis na positibong depinidong metriko. Eto ay konsepto ng distantansiya sa mga <a href="/w/index.php?title=Espasyong_tangent&action=edit&redlink=1" class="new" title="Espasyong tangent (hindi pa naisusulat)">espasyong tangent</a> sa bawat punto. Ang heometriyang Riemannian ay nilalahat ang heometriyang Euclidean sa mga espasyo na hindi kinakailangang patag bagaman ang mga ito'y katumbas pa rin ng espasyong Euclidean sa bawat puntong inpinitesimal o sa unang order ng aproksimasyon. Ang iba't ibang mga konsepto ng haba gaya ng <a href="/w/index.php?title=Arkong_haba&action=edit&redlink=1" class="new" title="Arkong haba (hindi pa naisusulat)">arkong haba</a> ng mga <a href="/wiki/Kurba_(heometriya)" class="mw-redirect" title="Kurba (heometriya)">kurba</a>, area ng mga rehiyong plano at <a href="/wiki/Bolyum" class="mw-redirect" title="Bolyum">bolyum</a> ng mga solido ay tumatanggap ng mga natural na <a href="/wiki/Analogo" class="mw-redirect" title="Analogo">analogo</a> ng heometriyang Riemannian. Ang nosyon ng direksiyonal na <a href="/w/index.php?title=Deribatib&action=edit&redlink=1" class="new" title="Deribatib (hindi pa naisusulat)">deribatib</a> ng isang <a href="/wiki/Punsiyon" class="mw-disambig" title="Punsiyon">punsiyon</a> sa <a href="/w/index.php?title=Multibariabulong_kalkulo&action=edit&redlink=1" class="new" title="Multibariabulong kalkulo (hindi pa naisusulat)">multibariabulong kalkulo</a> ay pinalawig sa heometriyang Riemannian sa nosyon ng mga <a href="/w/index.php?title=Kobariantong_deribatibo&action=edit&redlink=1" class="new" title="Kobariantong deribatibo (hindi pa naisusulat)">kobariantong deribatibo</a> ng isang <a href="/wiki/Tensor" title="Tensor">tensor</a>. Maraming mga konsepto at tekniko ng analisis at diperensiyal na ekwasyon ay nilahat sa kinalalagyan ng mga <a href="/wiki/Manipoldong_Riemannian" class="mw-redirect" title="Manipoldong Riemannian">manipoldong Riemannian</a>. </p><p>Ang nag-iingat ng distansiyang <a href="/w/index.php?title=Dipeomorpismo&action=edit&redlink=1" class="new" title="Dipeomorpismo (hindi pa naisusulat)">dipeomorpismo</a> sa pagitan ng mga manipoldong Riemannian ay tinatawag na isometriya. Ang nosyong ito ay inilalarawan ng lokal o sa mga maliit na kapitbahay ng mga punto. Ang anumang dalawang regular na mga kurba ay isometriko sa lokal. Gayunpaman, ang <a href="/w/index.php?title=Theorema_Egregium&action=edit&redlink=1" class="new" title="Theorema Egregium (hindi pa naisusulat)">Theorema Egregium</a> ni <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a> ay nagpapakita na sa mga surpasiyo, ang eksistensiya ng mga lokal na isometriya ay nagtatakda ng malakas ng kompatibilidad na mga kondisyon sa mga metriko nito: ang mga <a href="/w/index.php?title=Kurbadang_Gaussian&action=edit&redlink=1" class="new" title="Kurbadang Gaussian (hindi pa naisusulat)">kurbadang Gaussian</a> sa kaakibat na mga punto ay dapat pareho. Sa <a href="/w/index.php?title=Mataas_na_dimensiyon&action=edit&redlink=1" class="new" title="Mataas na dimensiyon (hindi pa naisusulat)">mataas na dimensiyon</a>, ang <a href="/w/index.php?title=Kurbadang_tensor_na_Riemann&action=edit&redlink=1" class="new" title="Kurbadang tensor na Riemann (hindi pa naisusulat)">kurbadang tensor na Riemann</a> ay isang mahalaga inbarianto sa mga punto na nauugnay sa isang <a href="/wiki/Manipoldong_Riemannian" class="mw-redirect" title="Manipoldong Riemannian">manipoldong Riemannian</a> na sumusukat kung paano kalapit ito sa pagiging patag. Ang isang mahalagang uri ng manipoldong Riemannian ang <a href="/w/index.php?title=Simetrikong_mga_espasyong_Riemannian&action=edit&redlink=1" class="new" title="Simetrikong mga espasyong Riemannian (hindi pa naisusulat)">simetrikong mga espasyong Riemannian</a> na ang kurbada ay hindi kinakailangang <a href="/wiki/Konstante" title="Konstante">konstante</a>. Ang mga ito ang pinakamalapit na analogo sa isang ordinaryong <a href="/wiki/Plano" class="mw-disambig" title="Plano">plano</a> at espasyo na itinuturing sa Euclidean at hindi-Euclidean na heometriya. </p> <div class="mw-heading mw-heading2"><h2 id="Heometriyang_Pseudo-Riemannian">Heometriyang Pseudo-Riemannian</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriyang_deribatibo&veaction=edit&section=3" title="Baguhin seksiyon: Heometriyang Pseudo-Riemannian" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriyang_deribatibo&action=edit&section=3" title="Edit section's source code: Heometriyang Pseudo-Riemannian"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ang <a href="/w/index.php?title=Manipoldong_Pseudo-Riemannian&action=edit&redlink=1" class="new" title="Manipoldong Pseudo-Riemannian (hindi pa naisusulat)">heometriyang Pseudo-Riemannian</a> ay isang kaso kung saan ang <a href="/wiki/Metrikong_tensor" title="Metrikong tensor">metrikong tensor</a> ay hindi kinakailangang positibo-depinido. Ang isang espesyal na kaso nito ang <a href="/w/index.php?title=Manipoldong_Lorentzian&action=edit&redlink=1" class="new" title="Manipoldong Lorentzian (hindi pa naisusulat)">manipoldong Lorentzian</a> na matematikal na basehan ng <a href="/w/index.php?title=Teoriyang_pangkahalatan_ng_relatibidad&action=edit&redlink=1" class="new" title="Teoriyang pangkahalatan ng relatibidad (hindi pa naisusulat)">teoriyang pangkahalatan ng relatibidad</a> ni <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Heometriyang_Finsler">Heometriyang Finsler</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriyang_deribatibo&veaction=edit&section=4" title="Baguhin seksiyon: Heometriyang Finsler" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriyang_deribatibo&action=edit&section=4" title="Edit section's source code: Heometriyang Finsler"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ang <a href="/w/index.php?title=Heometriyang_Finsler&action=edit&redlink=1" class="new" title="Heometriyang Finsler (hindi pa naisusulat)">Heometriyang Finsler</a> ay mayroong manipoldong Finsler bilang pangunahing obhekto ng pag-aaral. Eto ang <a href="/wiki/Diperensiyableng_manipoldo" class="mw-redirect" title="Diperensiyableng manipoldo">diperensiyableng manipoldo</a> na may <a href="/w/index.php?title=Metrikong_Finsler&action=edit&redlink=1" class="new" title="Metrikong Finsler (hindi pa naisusulat)">metrikong Finsler</a> o <a href="/w/index.php?title=Normang_Banach&action=edit&redlink=1" class="new" title="Normang Banach (hindi pa naisusulat)">normang Banach</a> na inilalarawan sa bawat <a href="/w/index.php?title=Espasyong_tangent&action=edit&redlink=1" class="new" title="Espasyong tangent (hindi pa naisusulat)">espasyong tangent</a>. Ang isang metrikong Finsler ay mas heneral na straktura kesa sa isang metrikong Riemannian. Ang isang strakturang Finsler sa isang manipoldong <i>M</i> ay isang punsiyong <i>F</i> : T<i>M</i> → [0,∞) kung saan: </p> <ol><li><i>F</i>(<i>x</i>, <i>my</i>) = <i>|m|F</i>(<i>x</i>,<i>y</i>) for all <i>x</i>, <i>y</i> sa T<i>M</i>,</li> <li><i>F</i> ay walang hangganang diperensiyable sa T<i>M</i> − {0},</li> <li>Ang bertikal na Hessian ng <i>F</i><sup>2</sup> ay positibo depinido.</li></ol> <div class="mw-heading mw-heading3"><h3 id="Heometriyang_Simplektiko">Heometriyang Simplektiko</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriyang_deribatibo&veaction=edit&section=5" title="Baguhin seksiyon: Heometriyang Simplektiko" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriyang_deribatibo&action=edit&section=5" title="Edit section's source code: Heometriyang Simplektiko"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ang <a href="/w/index.php?title=Heometriyang_simplektiko&action=edit&redlink=1" class="new" title="Heometriyang simplektiko (hindi pa naisusulat)">heometriyang simplektiko</a> ang pag-aaral ng mga <a href="/w/index.php?title=Manipoldong_simplektiko&action=edit&redlink=1" class="new" title="Manipoldong simplektiko (hindi pa naisusulat)">manipoldong simplektiko</a>. Ang isang halos na manipoldong simplektiko ay isang diperensiyableng manipoldo na may makinis na nag-iibang hindi <a href="/w/index.php?title=Dehenerado&action=edit&redlink=1" class="new" title="Dehenerado (hindi pa naisusulat)">dehenerado</a> simetrikong-lihis na anyong bilinyar sa bawat espasyong tangent o hindi deheneradong 2-anyong ω, na tinatawag na anyong simplektiko. Ang isang manipoldong simplektiko ay halos manipoldong simplektiko kung saan ang anyong simplektikong ω ay sarado: dω = 0. </p><p>Ang dipeomorpismo sa pagitan ng dalawang manipoldong simplektiko na nag-iingat sa anyong simplektiko ay tinatawag na simplektomorpismo. Ang hindi deheneradong simetrikong-libis na anyong bilinyar ay maaari lamang umiral sa even na mga dimensiyon na espasyong bektor kaya ang mga manipoldong simplektiko ay kinakailangang may even na dimensiyon. Sa dimensiyong 2, ang isang manipoldong simplektiko ay isa lamang surpasiyo na may anyong area at ang simplektomorpismo ay nag-iingat ng areang dipeomorpismo. Ang espasyong phase ng isang sistemang mekanikal ay isang manipoldong simplektiko at ang mga ito ay lumabas sa akda ni Lagrange sa analitikal na mekaniks at kalaunan ay sa pormulasyon nina Jacobi at Hamilton ng <a href="/wiki/Klasikong_mekaniks" class="mw-redirect" title="Klasikong mekaniks">klasikong mekaniks</a>. </p><p>Sa pagsasalungat sa heometriyang Riemannian kung saan ang kurbada ay nagbibigay ng lokal na inbarianto ng mga manipoldong Riemannian, ang teorema ni Darboux's ay nagsasaad na ang lahat ng mga manipoldong simplektiko ay lokal na isomorpiko. Ang mga tanging inbarianto ng isang manipoldong simplektio ay global sa kalikasan at ang mga aspetong topolohikal ay malamang ang <a href="/w/index.php?title=Teoremang_Poincar%C3%A9-Birkhoff&action=edit&redlink=1" class="new" title="Teoremang Poincaré-Birkhoff (hindi pa naisusulat)">teoremang Poincaré-Birkhoff</a> na kinonhektura ni <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a> at napatunayan ni <a href="/w/index.php?title=George_Birkhoff&action=edit&redlink=1" class="new" title="George Birkhoff (hindi pa naisusulat)">George Birkhoff</a> noong 1912. Ito ay nag-aangkin na kung ang mapang nag-iingat ng area ng isang annulus ay pinipilipit ang bawat hangganang komponente sa kabaligtarang direksiyon, kung gayon ang mapa ay may kahit papaanong dalawang nakapirmeng punto. </p> <div class="mw-heading mw-heading3"><h3 id="Heometriyang_kontakt">Heometriyang kontakt</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriyang_deribatibo&veaction=edit&section=6" title="Baguhin seksiyon: Heometriyang kontakt" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriyang_deribatibo&action=edit&section=6" title="Edit section's source code: Heometriyang kontakt"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ang <a href="/w/index.php?title=Heometriyang_kontakt&action=edit&redlink=1" class="new" title="Heometriyang kontakt (hindi pa naisusulat)">heometriyang kontakt</a> ay hinggil sa ilang mga manipoldo na may dimensiyong odd. Ito ay malapit sa heometriyang simplektiko at tulad ng huli, ito ay nagmula sa mga tanong ng <a href="/wiki/Klasikong_mekaniks" class="mw-redirect" title="Klasikong mekaniks">klasikong mekaniks</a>. Ang isang strakturang kontakt sa (2<i>n</i>+1)-dimensiyonal manipoldong <i>M</i> ay ibinibigay ng isang makinis na hiperplanong field na <i>H</i> sa <a href="/w/index.php?title=Bigkis_na_tangent&action=edit&redlink=1" class="new" title="Bigkis na tangent (hindi pa naisusulat)">bigkis na tangent</a>(tangent bundle) na pinakamalayo na maugnay sa mga lebel na hanay ng diperensiyable punsiyon sa <i>M</i> (ang teknikal na termino ay "buong buong hindi <a href="/wiki/Integral" class="mw-redirect" title="Integral">integrableng</a> tangent hiperplanong distribusyon" o "completely nonintegrable tangent hyperplane distribution"). Sa bawat malapit sa puntong <i>p</i>, ang isang hiperplanong distribusyon ay matutukoy sa pamamagitan ng wala saanmang naglalahong <a href="/w/index.php?title=Anyong_diperensiyal&action=edit&redlink=1" class="new" title="Anyong diperensiyal (hindi pa naisusulat)">1-form</a> na <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> na uniko(unique) hanggang sa multiplikasyon ng isang wala saanmang naglalahong punsiyong: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{p}=\ker \alpha _{p}\subset T_{p}M.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mi>ker</mi> <mo>⁡</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>⊂</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mi>M</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{p}=\ker \alpha _{p}\subset T_{p}M.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ccb331c20d96424b23909681b67f7df0c0f3732" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.798ex; height:2.843ex;" alt="{\displaystyle H_{p}=\ker \alpha _{p}\subset T_{p}M.}"></span></dd></dl> <p>Ang lokal na 1-anyo sa <i>M</i> ay isang anyong kontakt kung ang restriksiyon ng <a href="/w/index.php?title=Panlabas_na_deribatibo&action=edit&redlink=1" class="new" title="Panlabas na deribatibo (hindi pa naisusulat)">panlabas na deribatibo</a> nito sa <i>H</i> ay hindi deheneradong 2-anyo kaya ito ay naghihimok ng isang simplektikong straktura sa <i>H</i><sub><i>p</i></sub> sa bawat punto. Kung ang distribusyong <i>H</i> ay maaaring ilarawan ng isang global na 1-anyong <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span>, ang anyong ito ay kontakt kung at tanging kung ang tuktok na anyong dimensiyonal na </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha \wedge (d\alpha )^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>∧</mo> <mo stretchy="false">(</mo> <mi>d</mi> <mi>α</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha \wedge (d\alpha )^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/baa14d26d0b8f92739361626b27e1ecf55d1abfa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.801ex; height:2.843ex;" alt="{\displaystyle \alpha \wedge (d\alpha )^{n}}"></span></dd></dl> <p>ay isang <a href="/w/index.php?title=Anyong_bolyum&action=edit&redlink=1" class="new" title="Anyong bolyum (hindi pa naisusulat)">anyong bolyum</a> sa <i>M</i> o hindi naglalaho saan man. Ang isang analogong kontakt ng <a href="/w/index.php?title=Teoremang_Darboux&action=edit&redlink=1" class="new" title="Teoremang Darboux (hindi pa naisusulat)">teoremang Darboux</a> ay nagsasaad na: lahat ng mga strakturang kontakt sa isang odd-dimensiyonal na manipoldo ay lokal na isomorpiko at maaaring gawing isang lokal na anyong normal sa pamamamagitan ng nararapat na mapagpipiliang sistemang koordinado. </p> <div class="mw-heading mw-heading3"><h3 id="Heometriyang_kompleks_at_Kähler"><span id="Heometriyang_kompleks_at_K.C3.A4hler"></span>Heometriyang kompleks at Kähler</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriyang_deribatibo&veaction=edit&section=7" title="Baguhin seksiyon: Heometriyang kompleks at Kähler" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriyang_deribatibo&action=edit&section=7" title="Edit section's source code: Heometriyang kompleks at Kähler"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ang kompleks na diperensiyal na heometriya ay pag-aaral ng mga <a href="/w/index.php?title=Manipoldong_kompleks&action=edit&redlink=1" class="new" title="Manipoldong kompleks (hindi pa naisusulat)">manipoldong kompleks</a>. Ang isang halos na manipoldong kompleks ay isang real na manipoldong <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> na may <a href="/wiki/Tensor" title="Tensor">tensor</a> ng uring (1,1) o <a href="/w/index.php?title=Bigkis_na_bektor&action=edit&redlink=1" class="new" title="Bigkis na bektor (hindi pa naisusulat)">endomorpismong bigkis na bektor</a>(na tinawag na halos kompleks na straktura) </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J:TM\rightarrow TM}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>:</mo> <mi>T</mi> <mi>M</mi> <mo stretchy="false">→</mo> <mi>T</mi> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J:TM\rightarrow TM}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5cf6a2e36448c0cf0b07478df0ad18942d13b66c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.18ex; height:2.176ex;" alt="{\displaystyle J:TM\rightarrow TM}"></span>, such that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J^{2}=-1\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J^{2}=-1\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/362784524617409b6d76ed3b72dcff2166b2deaf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.036ex; height:2.843ex;" alt="{\displaystyle J^{2}=-1\,}"></span>.</dd></dl> <p>Sumusunod sa depinsiyong ito na ang halos kompleks na manipoldo ay even dimensiyonal. </p><p>Ang isang halos kompleks na manipoldo ay tinatawag na kompleks kung ang <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{J}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>J</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{J}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9afb80d5b99e54da4b62e70ed5af7a7941c27ee1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.4ex; height:2.509ex;" alt="{\displaystyle N_{J}=0}"></span>, kung saan ang <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{J}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>J</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{J}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9d972b42cc71fd31bd2f0e9526844ead9b9f0d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.139ex; height:2.509ex;" alt="{\displaystyle N_{J}}"></span> ay tensor na uring(2,1) na kaugnay ng <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/359e4f407b49910e02c27c2f52e87a36cd74c053" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\displaystyle J}"></span> na tinatawag na <a href="/w/index.php?title=Tensor_na_Nijenhuis&action=edit&redlink=1" class="new" title="Tensor na Nijenhuis (hindi pa naisusulat)">tensor na Nijenhuis</a> (o minsan ay <i>torsiyon</i>). </p><p>Ang isang halos kompleks na manipoldo ay kompleks kung at tanging kung tumatanggap ito ng holomorpikong<a href="/w/index.php?title=Atlas_(topolohiya)&action=edit&redlink=1" class="new" title="Atlas (topolohiya) (hindi pa naisusulat)">atlas na koordinado</a>. </p><p>Ang isang <a href="/w/index.php?title=Manipoldong_Hermitian&action=edit&redlink=1" class="new" title="Manipoldong Hermitian (hindi pa naisusulat)">manipoldong Hermitian</a> ay ibinibigay ng halos kompleks na strakturang <i>J</i>, kasama ang <a href="/w/index.php?title=Metrikong_riemannian&action=edit&redlink=1" class="new" title="Metrikong riemannian (hindi pa naisusulat)">metrikong riemannian</a> na <i>g</i> na sumasapat sa kondisyong kompatibilidad </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g(JX,JY)=g(X,Y)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>J</mi> <mi>X</mi> <mo>,</mo> <mi>J</mi> <mi>Y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(JX,JY)=g(X,Y)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92144818686f197a235e95849a311a6600407772" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.853ex; height:2.843ex;" alt="{\displaystyle g(JX,JY)=g(X,Y)\,}"></span>.</dd></dl> <p>Ang halos strakturang hermitian ay natural na naglalarawan ng <a href="/w/index.php?title=Anyong_diperensiyal&action=edit&redlink=1" class="new" title="Anyong diperensiyal (hindi pa naisusulat)">2-anyong diperensiyal</a>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{J,g}(X,Y):=g(JX,Y)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>J</mi> <mo>,</mo> <mi>g</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo stretchy="false">)</mo> <mo>:=</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>J</mi> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{J,g}(X,Y):=g(JX,Y)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66ff04b5c58696b8576763b63630e8252069b374" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:23.878ex; height:3.009ex;" alt="{\displaystyle \omega _{J,g}(X,Y):=g(JX,Y)\,}"></span>.</dd></dl> <p>Ang mga sumusunod na dalawang kondisyon ay magkatumbas: </p><p><br /> </p> <ol><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{J}=0{\mbox{ and }}d\omega =0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>J</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> and </mtext> </mstyle> </mrow> <mi>d</mi> <mi>ω</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{J}=0{\mbox{ and }}d\omega =0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/363b0cf5bc37f99239a4d4148b7efef5389c99e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.618ex; height:2.509ex;" alt="{\displaystyle N_{J}=0{\mbox{ and }}d\omega =0\,}"></span></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla J=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mi>J</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla J=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e488bfae1b002702f428478dd1e1987240e2f37" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.055ex; height:2.176ex;" alt="{\displaystyle \nabla J=0\,}"></span></li></ol> <p>kung saan ang <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3d0e93b78c50237f9ea83d027e4ebbdaef354b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.176ex;" alt="{\displaystyle \nabla }"></span> ang <a href="/w/index.php?title=Koneksiyong_Levi-Civita&action=edit&redlink=1" class="new" title="Koneksiyong Levi-Civita (hindi pa naisusulat)">koneksiyong Levi-Civita</a> ng <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\displaystyle g}"></span>. Sa kasong ito, ang <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (J,g)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>J</mi> <mo>,</mo> <mi>g</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (J,g)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c254d160bf244c5e8f17dfe4f0289d29cd7df98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.431ex; height:2.843ex;" alt="{\displaystyle (J,g)}"></span> ay tinatawag na <a href="/w/index.php?title=Manipoldong_K%C3%A4hler&action=edit&redlink=1" class="new" title="Manipoldong Kähler (hindi pa naisusulat)">manipoldong Kähler</a> at ang manipoldong Kähler ay mayroong strakturang Kähler. Sa partikular, ang manipoldong Kähler ay parehong kompleks at simplektikong manipoldo. Ang malaking klase ng mga manipoldong Kähler(ang klase ng <a href="/w/index.php?title=Manipoldong_Hodge&action=edit&redlink=1" class="new" title="Manipoldong Hodge (hindi pa naisusulat)">manipoldong Hodge</a>) ay ibinibigay ng lahat ng makinis na <a href="/wiki/Alhebraikong_heometriya" class="mw-redirect" title="Alhebraikong heometriya">kompleks na prohektibong mga bariedad</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Heometriyang_CR">Heometriyang CR</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriyang_deribatibo&veaction=edit&section=8" title="Baguhin seksiyon: Heometriyang CR" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriyang_deribatibo&action=edit&section=8" title="Edit section's source code: Heometriyang CR"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ang heometriyang CR ang pag-aaral ng mga intrinsik na heometriya ng mga hangganan ng mga sakop sa mga manipoldong kompleks. </p> <div class="mw-heading mw-heading3"><h3 id="Topolohiyang_diperensiyal">Topolohiyang diperensiyal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriyang_deribatibo&veaction=edit&section=9" title="Baguhin seksiyon: Topolohiyang diperensiyal" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriyang_deribatibo&action=edit&section=9" title="Edit section's source code: Topolohiyang diperensiyal"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ang <a href="/wiki/Topolohiyang_diperensiyal" class="mw-redirect" title="Topolohiyang diperensiyal">topolohiyang diperensiyal</a> ang pag-aaral ng (global) na mga inbariantong heometriko na walang metriko o anyong simplektiko. Ito ay nagsisimula mula sa mga natural na operasyon gaya ng <a href="/w/index.php?title=Deribatibong_Lie&action=edit&redlink=1" class="new" title="Deribatibong Lie (hindi pa naisusulat)">deribatibong Lie</a> ng natural na mga bigkis na bektor at diperensiyal ng mga anyong de Rham. Bukod sa Lie alhebroid ang Kourant alhebroid ay nagsimulang gumanap ng mas mahalagang papel. </p> <div class="mw-heading mw-heading3"><h3 id="Mga_grupong_Lie">Mga grupong Lie</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriyang_deribatibo&veaction=edit&section=10" title="Baguhin seksiyon: Mga grupong Lie" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriyang_deribatibo&action=edit&section=10" title="Edit section's source code: Mga grupong Lie"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ang isang grupong Lie ay isang grupo sa kategorya ng mga manipoldong makinis o bukod sa mga katangiang alhebraiko, eto ay nagtatamasa ng mga diperensiyal na heometrikong mga katangian. Ang pinakahalatang konstruksiyon ay ng alhebrang Lie na isang espasyong tangent sa unit na may braket Lie sa pagitan ng mga kaliweteng-inbariantong bektor field. 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href="/w/index.php?title=Padron:Areas_of_mathematics&action=edit&redlink=1" class="new" title="Padron:Areas of mathematics (hindi pa naisusulat)"><abbr title="Tingnan ang padron">t</abbr></a></li><li class="nv-usapan"><a href="/w/index.php?title=Usapang_padron:Areas_of_mathematics&action=edit&redlink=1" class="new" title="Usapang padron:Areas of mathematics (hindi pa naisusulat)"><abbr title="Pag-usapan ang padron">u</abbr></a></li><li class="nv-baguhin"><a class="external text" href="https://tl.wikipedia.org/w/index.php?title=Padron:Areas_of_mathematics&action=edit"><abbr title="Baguhin ang padron">b</abbr></a></li></ul></div><div id="Matematika_(sipnayan)" style="font-size:114%;margin:0 4em"><a href="/wiki/Matematika" title="Matematika">Matematika</a> <small>(sipnayan)</small></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Kasaysayan_ng_matematika" title="Kasaysayan ng matematika">Kasaysayan</a></li> <li><a href="/wiki/Pilosopiya_ng_matematika" title="Pilosopiya ng matematika">Pilosopiya</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/w/index.php?title=Haligi_ng_matematika&action=edit&redlink=1" class="new" title="Haligi ng matematika (hindi pa naisusulat)">Haligi</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i>Teorya ng</i> <ul><li><a href="/wiki/Teorya_ng_impormasyon" title="Teorya ng impormasyon">impormasyon</a></li> <li><a href="/wiki/Teorya_ng_kategorya" title="Teorya ng kategorya">kategorya</a></li> <li><a href="/wiki/Teorya_ng_pangkat" title="Teorya ng pangkat">pangkat</a></li> <li><a href="/w/index.php?title=Teorya_ng_uri&action=edit&redlink=1" class="new" title="Teorya ng uri (hindi pa naisusulat)">uri</a></li></ul></li> <li><a href="/wiki/Lohikang_matematikal" title="Lohikang matematikal">Lohika</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Alhebra" title="Alhebra">Alhebra</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alhebrang_basal" title="Alhebrang basal">Basal</a></li> <li><a href="/wiki/Alhebrang_elementaryo" title="Alhebrang elementaryo">Elementaryo</a></li> <li><a href="/w/index.php?title=Alhebrang_homolohika&action=edit&redlink=1" class="new" title="Alhebrang homolohika (hindi pa naisusulat)">Homolohika</a></li> <li><a href="/w/index.php?title=Alhebrang_komutatibo&action=edit&redlink=1" class="new" title="Alhebrang komutatibo (hindi pa naisusulat)">Komutatibo</a></li> <li><a href="/wiki/Alhebrang_linyar" title="Alhebrang linyar">Linyar</a> <ul><li><a href="/wiki/Alhebrang_multilinyar" title="Alhebrang multilinyar">multi</a></li></ul></li> <li><a href="/w/index.php?title=Alhebrang_pangkalahatan&action=edit&redlink=1" class="new" title="Alhebrang pangkalahatan (hindi pa naisusulat)">Pangkalahatan</a></li> <li><a href="/wiki/Teorya_ng_grupo" title="Teorya ng grupo">Teorya ng grupo</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Pagsusuring_matematikal" title="Pagsusuring matematikal">Pagsusuri</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ekwasyong_diperensiyal" title="Ekwasyong diperensiyal">Ekwasyong diperensiyal</a></li> <li><a href="/wiki/Kalkulo" class="mw-redirect" title="Kalkulo">Kalkulo</a></li> <li><i>Pagsusuring...</i> <ul><li><a href="/w/index.php?title=Pagsusuring_harmoniko&action=edit&redlink=1" class="new" title="Pagsusuring harmoniko (hindi pa naisusulat)">harmoniko</a></li> <li><a href="/w/index.php?title=Pagsusuring_komplikado&action=edit&redlink=1" class="new" title="Pagsusuring komplikado (hindi pa naisusulat)">komplikado</a> <ul><li><a href="/w/index.php?title=Pagsusuring_hiperkomplikado&action=edit&redlink=1" class="new" title="Pagsusuring hiperkomplikado (hindi pa naisusulat)">hiper</a></li></ul></li> <li><a href="/wiki/Pagsusuring_punsiyonal" title="Pagsusuring punsiyonal">punsiyon</a></li> <li><a href="/w/index.php?title=Pagsusuring_tunay&action=edit&redlink=1" class="new" title="Pagsusuring tunay (hindi pa naisusulat)">tunay</a></li></ul></li> <li><a href="/wiki/Sukat_(matematika)" title="Sukat (matematika)">Teorya ng sukat</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Matematikang_diskreto" title="Matematikang diskreto">Diskreto</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kombinatorika" title="Kombinatorika">Kombinatorika</a></li> <li><i>Teorya ng...</i> <ul><li><a href="/w/index.php?title=Teorya_ng_ayos&action=edit&redlink=1" class="new" title="Teorya ng ayos (hindi pa naisusulat)">ayos</a></li> <li><a href="/wiki/Teorya_ng_grap" title="Teorya ng grap">grap</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Heometriya" title="Heometriya">Heometriya</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Heometriyang_alhebraiko" title="Heometriyang alhebraiko">Alhebraiko</a></li> <li><a href="/w/index.php?title=Heometriyang_aritmetiko&action=edit&redlink=1" class="new" title="Heometriyang aritmetiko (hindi pa naisusulat)">Aritmetiko</a></li> <li><a class="mw-selflink selflink">Deribatibo</a></li> <li><a href="/wiki/Heometriyang_diskreto" class="mw-redirect" title="Heometriyang diskreto">Diskreto</a></li> <li><a href="/w/index.php?title=Heometriyang_Euclides&action=edit&redlink=1" class="new" title="Heometriyang Euclides (hindi pa naisusulat)">Euclides</a></li> <li><a href="/w/index.php?title=Heometriyang_natatapos&action=edit&redlink=1" class="new" title="Heometriyang natatapos (hindi pa naisusulat)">Natatapos</a></li> <li><a href="/wiki/Heometriyang_pasuri" title="Heometriyang pasuri">Pasuri</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Teorya_ng_bilang" title="Teorya ng bilang">Teorya ng bilang</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Alhebraikong_teorya_ng_bilang&action=edit&redlink=1" class="new" title="Alhebraikong teorya ng bilang (hindi pa naisusulat)">Alhebraiko</a></li> <li><a href="/wiki/Aritmetika" title="Aritmetika">Aritmetika</a></li> <li><a href="/w/index.php?title=Heometriyang_diopantika&action=edit&redlink=1" class="new" title="Heometriyang diopantika (hindi pa naisusulat)">Heometriyang diopantika</a></li> <li><a href="/w/index.php?title=Pasuring_teorya_ng_bilang&action=edit&redlink=1" class="new" title="Pasuring teorya ng bilang (hindi pa naisusulat)">Pasuri</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Topolohiya" title="Topolohiya">Topolohiya</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Topolohiyang_alhebraiko&action=edit&redlink=1" class="new" title="Topolohiyang alhebraiko (hindi pa naisusulat)">Alhebraiko</a></li> <li><a href="/wiki/Topolohiyang_diperensiyal" class="mw-redirect" title="Topolohiyang diperensiyal">Diperensiyal</a></li> <li><a href="/w/index.php?title=Topolohiyang_heometriko&action=edit&redlink=1" class="new" title="Topolohiyang heometriko (hindi pa naisusulat)">Heometriko</a></li> <li><a href="/w/index.php?title=Homotopiya&action=edit&redlink=1" class="new" title="Homotopiya (hindi pa naisusulat)">Homotopiya</a> <ul><li><a href="/w/index.php?title=Teorya_ng_homotopiya&action=edit&redlink=1" class="new" title="Teorya ng homotopiya (hindi pa naisusulat)">teorya</a></li></ul></li> <li><a href="/w/index.php?title=Topolohiyang_pangkalahatan&action=edit&redlink=1" class="new" title="Topolohiyang pangkalahatan (hindi pa naisusulat)">Pangkalahatan</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Matematikang_nalalapat" class="mw-redirect" title="Matematikang nalalapat">Nalalapat</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Agham_pansistema&action=edit&redlink=1" class="new" title="Agham pansistema (hindi pa naisusulat)">Agham pansistema</a> <ul><li><a href="/w/index.php?title=Pananaliksik_pang-operasyon&action=edit&redlink=1" class="new" title="Pananaliksik pang-operasyon (hindi pa naisusulat)">pananaliksik pang-operasyon</a></li> <li><i>teorya ng...</i> <ul><li><a href="/wiki/Teorya_ng_kontrol" title="Teorya ng kontrol">kontrol</a></li> <li><a href="/wiki/Teorya_ng_laro" title="Teorya ng laro">laro</a></li></ul></li></ul></li> <li><a href="/wiki/Estadistika" title="Estadistika">Estadistika</a></li> <li><i>Matematikang...</i> <ul><li><a href="/wiki/Matematikang_pangbiolohiya" title="Matematikang pangbiolohiya">biolohiya</a></li> <li><a href="/wiki/Matematikang_pang-ekonomika" title="Matematikang pang-ekonomika">ekonomika</a></li> <li><a href="/w/index.php?title=Matematikang_pang-estadistika&action=edit&redlink=1" class="new" title="Matematikang pang-estadistika (hindi pa naisusulat)">estadistika</a></li> <li><a href="/w/index.php?title=Matematikang_pang-inhinyera&action=edit&redlink=1" class="new" title="Matematikang pang-inhinyera (hindi pa naisusulat)">inhinyera</a></li> <li><a href="/w/index.php?title=Matematikang_pangkimika&action=edit&redlink=1" class="new" title="Matematikang pangkimika (hindi pa naisusulat)">kimika</a></li> <li><a href="/w/index.php?title=Matematikang_pampananalapi&action=edit&redlink=1" class="new" title="Matematikang pampananalapi (hindi pa naisusulat)">pananalapi</a></li> <li><a href="/wiki/Matematikang_pampisika" title="Matematikang pampisika">pisika</a></li> <li><a href="/w/index.php?title=Matematikang_pangsikolohiya&action=edit&redlink=1" class="new" title="Matematikang pangsikolohiya (hindi pa naisusulat)">sikolohiya</a></li> <li><a href="/w/index.php?title=Matematikang_pangsosyolohiya&action=edit&redlink=1" class="new" title="Matematikang pangsosyolohiya (hindi pa naisusulat)">sosyolohiya</a></li></ul></li> <li><a href="/wiki/Teorya_ng_probabilidad" title="Teorya ng probabilidad">Probabilidad</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Matematikang_komputasyonal" title="Matematikang komputasyonal">Komputasyonal</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Alhebrang_pangkompyuter&action=edit&redlink=1" class="new" title="Alhebrang pangkompyuter (hindi pa naisusulat)">Alhebrang pangkompyuter</a></li> <li><a href="/wiki/Agham_pangkompyuter" title="Agham pangkompyuter">Agham pangkompyuter</a></li> <li><a href="/wiki/Optimisasyong_matematikal" title="Optimisasyong matematikal">Optimisasyon</a></li> <li><a href="/wiki/Pagsusuring_pambilang" title="Pagsusuring pambilang">Pagsusuring pambilang</a></li> <li><i>Teorya ng...</i> <ul><li><a href="/wiki/Teorya_ng_komputasyon" title="Teorya ng komputasyon">komputasyon</a></li> <li><a href="/wiki/Teorya_ng_komputasyonal_na_komplehidad" title="Teorya ng komputasyonal na komplehidad">komputasyonal na komplehidad</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Kaugnay</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Matematika_bilang_libangan&action=edit&redlink=1" class="new" title="Matematika bilang libangan (hindi pa naisusulat)">Matematika bilang libangan</a></li> <li><a href="/w/index.php?title=Mathematika_at_sining&action=edit&redlink=1" class="new" title="Mathematika at sining (hindi pa naisusulat)">Mathematika at sining</a></li> <li><a href="/w/index.php?title=Matematikang_di-pormal&action=edit&redlink=1" class="new" title="Matematikang di-pormal (hindi pa naisusulat)">Matematikang di-pormal</a></li> <li><a href="/wiki/Matematiko" title="Matematiko">Matematiko</a> <ul><li><a href="/w/index.php?title=Listahan_ng_mga_matematiko&action=edit&redlink=1" class="new" title="Listahan ng mga matematiko (hindi pa naisusulat)">listahan</a></li></ul></li> <li><a href="/w/index.php?title=Pagtuturo_ng_matematika&action=edit&redlink=1" class="new" title="Pagtuturo ng matematika (hindi pa naisusulat)">Pagtuturo ng matematika</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span typeof="mw:File"><span title="Kategorya"><img alt="Kategorya" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Folder_Hexagonal_Icon.svg/16px-Folder_Hexagonal_Icon.svg.png" decoding="async" width="16" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Folder_Hexagonal_Icon.svg/24px-Folder_Hexagonal_Icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/48/Folder_Hexagonal_Icon.svg/32px-Folder_Hexagonal_Icon.svg.png 2x" data-file-width="36" data-file-height="31" /></span></span> <b><a href="/wiki/Kategorya:Matematika" title="Kategorya:Matematika">Kategorya</a></b></li> <li><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Symbol_question.svg/16px-Symbol_question.svg.png" decoding="async" width="16" height="16" class="mw-file-element" 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Pambansa</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="uid"><abbr title="Géométrie différentielle"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb133188233">Pransiya</a></abbr></span></li> <li><span class="uid"><abbr title="Géométrie différentielle"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb133188233">Datos ng BnF</a></abbr></span></li> <li><span class="uid"><a rel="nofollow" class="external text" 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rel="nofollow" class="external text" href="http://esu.com.ua/search_articles.php?id=24415">Encyclopedia of Modern Ukraine</a></span></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Kinuha sa "<a dir="ltr" href="https://tl.wikipedia.org/w/index.php?title=Heometriyang_deribatibo&oldid=2033228">https://tl.wikipedia.org/w/index.php?title=Heometriyang_deribatibo&oldid=2033228</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Natatangi:Mga_kategorya" title="Natatangi:Mga kategorya">Kategorya</a>: <ul><li><a href="/wiki/Kategorya:Diperensiyal_na_heometriya" title="Kategorya:Diperensiyal na heometriya">Diperensiyal na heometriya</a></li></ul></div><div id="mw-hidden-catlinks" 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