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Je dostupný v 38 jazycích" > <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-38" 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">38 jazyků</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%B1%D9%8A%D9%85%D8%A7%D9%86%D9%8A%D8%A9" title="هندسة ريمانية – arabština" lang="ar" hreflang="ar" data-title="هندسة ريمانية" data-language-autonym="العربية" data-language-local-name="arabština" 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_de_Riemann" title="Xeometría de Riemann – asturština" lang="ast" hreflang="ast" data-title="Xeometría de Riemann" data-language-autonym="Asturianu" data-language-local-name="asturština" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Riman_h%C9%99nd%C9%99s%C9%99si" title="Riman həndəsəsi – ázerbájdžánština" lang="az" hreflang="az" data-title="Riman həndəsəsi" data-language-autonym="Azərbaycanca" data-language-local-name="ázerbájdžánština" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Риманова геометрия – bulharština" lang="bg" hreflang="bg" data-title="Риманова геометрия" data-language-autonym="Български" data-language-local-name="bulharština" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Geometria_riemanniana" title="Geometria riemanniana – katalánština" lang="ca" hreflang="ca" data-title="Geometria riemanniana" data-language-autonym="Català" data-language-local-name="katalánština" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D0%B9%C4%95" title="Риман геометрийĕ – čuvaština" lang="cv" hreflang="cv" data-title="Риман геометрийĕ" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" 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/Riemannsk_geometri" title="Riemannsk geometri – dánština" lang="da" hreflang="da" data-title="Riemannsk geometri" data-language-autonym="Dansk" data-language-local-name="dánština" 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/Riemannsche_Geometrie" title="Riemannsche Geometrie – němčina" lang="de" hreflang="de" data-title="Riemannsche Geometrie" data-language-autonym="Deutsch" data-language-local-name="němčina" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Riemannian_geometry" title="Riemannian geometry – angličtina" lang="en" hreflang="en" data-title="Riemannian geometry" data-language-autonym="English" data-language-local-name="angličtina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Geometr%C3%ADa_de_Riemann" title="Geometría de Riemann – španělština" lang="es" hreflang="es" data-title="Geometría de Riemann" data-language-autonym="Español" data-language-local-name="španělština" 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/Riemanni_geomeetria" title="Riemanni geomeetria – estonština" lang="et" hreflang="et" data-title="Riemanni geomeetria" data-language-autonym="Eesti" data-language-local-name="estonština" 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/Riemannen_geometria" title="Riemannen geometria – baskičtina" lang="eu" hreflang="eu" data-title="Riemannen geometria" data-language-autonym="Euskara" data-language-local-name="baskičtina" 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%B1%DB%8C%D9%85%D8%A7%D9%86%DB%8C" title="هندسه ریمانی – perština" lang="fa" hreflang="fa" data-title="هندسه ریمانی" data-language-autonym="فارسی" data-language-local-name="perština" 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/Riemannin_geometria" title="Riemannin geometria – finština" lang="fi" hreflang="fi" data-title="Riemannin geometria" data-language-autonym="Suomi" data-language-local-name="finština" 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_riemannienne" title="Géométrie riemannienne – francouzština" lang="fr" hreflang="fr" data-title="Géométrie riemannienne" data-language-autonym="Français" data-language-local-name="francouzština" 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_de_Riemann" title="Xeometría de Riemann – galicijština" lang="gl" hreflang="gl" data-title="Xeometría de Riemann" data-language-autonym="Galego" data-language-local-name="galicijština" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B0%E0%A5%80%E0%A4%AE%E0%A4%BE%E0%A4%A8%E0%A5%80_%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="रीमानी ज्यामिति – hindština" lang="hi" hreflang="hi" data-title="रीमानी ज्यामिति" data-language-autonym="हिन्दी" data-language-local-name="hindština" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8C%D5%AB%D5%B4%D5%A1%D5%B6%D5%B5%D5%A1%D5%B6_%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="Ռիմանյան երկրաչափություն – arménština" lang="hy" hreflang="hy" data-title="Ռիմանյան երկրաչափություն" data-language-autonym="Հայերեն" data-language-local-name="arménština" 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_Riemann" title="Geometri Riemann – indonéština" lang="id" hreflang="id" data-title="Geometri Riemann" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéština" 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_riemanniana" title="Geometria riemanniana – italština" lang="it" hreflang="it" data-title="Geometria riemanniana" data-language-autonym="Italiano" data-language-local-name="italština" 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/%E3%83%AA%E3%83%BC%E3%83%9E%E3%83%B3%E5%B9%BE%E4%BD%95%E5%AD%A6" title="リーマン幾何学 – japonština" lang="ja" hreflang="ja" data-title="リーマン幾何学" data-language-autonym="日本語" data-language-local-name="japonština" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Риман геометриясы – kazaština" lang="kk" hreflang="kk" data-title="Риман геометриясы" data-language-autonym="Қазақша" data-language-local-name="kazaština" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A6%AC%EB%A7%8C_%EA%B8%B0%ED%95%98%ED%95%99" title="리만 기하학 – korejština" lang="ko" hreflang="ko" data-title="리만 기하학" data-language-autonym="한국어" data-language-local-name="korejština" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Riemann-meetkunde" title="Riemann-meetkunde – nizozemština" lang="nl" hreflang="nl" data-title="Riemann-meetkunde" data-language-autonym="Nederlands" data-language-local-name="nizozemština" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Riemanns_differensialgeometri" title="Riemanns differensialgeometri – norština (bokmål)" lang="nb" hreflang="nb" data-title="Riemanns differensialgeometri" data-language-autonym="Norsk bokmål" data-language-local-name="norština (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B0%E0%A9%80%E0%A8%AE%E0%A8%BE%E0%A8%A8%E0%A9%80%E0%A8%85%E0%A8%A8_%E0%A8%9C%E0%A9%80%E0%A8%93%E0%A8%AE%E0%A9%88%E0%A8%9F%E0%A9%8D%E0%A8%B0%E0%A9%80" title="ਰੀਮਾਨੀਅਨ ਜੀਓਮੈਟ੍ਰੀ – paňdžábština" lang="pa" hreflang="pa" data-title="ਰੀਮਾਨੀਅਨ ਜੀਓਮੈਟ੍ਰੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="paňdžábština" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Geometria_de_Riemann" title="Geometria de Riemann – portugalština" lang="pt" hreflang="pt" data-title="Geometria de Riemann" data-language-autonym="Português" data-language-local-name="portugalština" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Риманова геометрия – ruština" lang="ru" hreflang="ru" data-title="Риманова геометрия" data-language-autonym="Русский" data-language-local-name="ruština" 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/Riemannova_geometrija" title="Riemannova geometrija – srbochorvatština" lang="sh" hreflang="sh" data-title="Riemannova geometrija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbochorvatština" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Rimanova_geometrija" title="Rimanova geometrija – srbština" lang="sr" hreflang="sr" data-title="Rimanova geometrija" data-language-autonym="Српски / srpski" data-language-local-name="srbština" 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/Riemanngeometri" title="Riemanngeometri – švédština" lang="sv" hreflang="sv" data-title="Riemanngeometri" data-language-autonym="Svenska" data-language-local-name="švédština" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Heometriyang_Riemanniano" title="Heometriyang Riemanniano – tagalog" lang="tl" hreflang="tl" data-title="Heometriyang Riemanniano" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Riemann_geometrisi" title="Riemann geometrisi – turečtina" 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class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Vzhled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skrýt</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Z Wikipedie, otevřené encyklopedie</div> </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="cs" dir="ltr"><p><b>Riemannova (riemannovská) geometrie</b> je oblast <a href="/wiki/Diferenci%C3%A1ln%C3%AD_geometrie" title="Diferenciální geometrie">diferenciální geometrie</a>, která se zabývá studiem <a href="/wiki/Riemann%C5%AFv_prostor" title="Riemannův prostor">Riemannových prostorů</a>. Riemannův prostor je hladká <a href="/wiki/Varieta_(matematika)" title="Varieta (matematika)">varieta</a>, na které lze měřit velikosti a úhly <a href="/wiki/Te%C4%8Dn%C3%BD_vektor" title="Tečný vektor">tečných vektorů</a>, měřit délky křivek a paralelně <a href="/wiki/Paraleln%C3%AD_p%C5%99enos_(geometrie)" title="Paralelní přenos (geometrie)">přenášet vektory</a>. </p><p>Riemannova geometrie vznikla v polovině 19. století ve snaze zobecnit a klasifikovat nové neeukleidovské geometrie jako jsou <a href="/wiki/Hyperbolick%C3%A1_geometrie" title="Hyperbolická geometrie">hyperbolická</a> a <a href="/wiki/Sf%C3%A9rick%C3%A1_geometrie" title="Sférická geometrie">sférická geometrie</a>. Tyto geometrie se v Riemannově geometrii vyskytují jako plochy s nenulovou konstantní křivostí, přičemž eukleidovská geometrie se dá modelovat jako Riemannova geometrie s nulovou křivostí. </p> <div class="mw-heading mw-heading2"><h2 id="Pseudoriemannova_geometrie">Pseudoriemannova geometrie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Riemannova_geometrie&veaction=edit&section=1" title="Editace sekce: Pseudoriemannova geometrie" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Riemannova_geometrie&action=edit&section=1" title="Editovat zdrojový kód sekce Pseudoriemannova geometrie"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O Riemannově geometrii se obvykle hovoří pouze v případě, že všechny nenulové tečné vektory mají kladnou velikost. Jinými slovy, <a href="/wiki/Metrick%C3%BD_tenzor" title="Metrický tenzor">metrický tenzor</a> je pozitivně definitní. Je-li <a href="/w/index.php?title=Indefinitn%C3%AD_forma&action=edit&redlink=1" class="new" title="Indefinitní forma (stránka neexistuje)">indefinitní</a>, což je příklad <a href="/wiki/%C4%8Casoprostor" title="Časoprostor">prostoročasu</a> v <a href="/wiki/Obecn%C3%A1_teorie_relativity" title="Obecná teorie relativity">obecné teorii relativity</a>, pak se hovoří o <b>pseudoRiemannově (pseudoriemannovské) geometrii</b>. Podkladový prostor se pak nazývá pseudoriemannova varieta. Pseudoriemannova geometrie našla uplatnění především v Einsteinově <a href="/wiki/Obecn%C3%A1_teorie_relativity" title="Obecná teorie relativity">obecné teorii relativity</a>, ve které slouží jako model časoprostoru. Rovnice obecné teorie relativity pak dávají do souvislosti hmotu a zakřivení časoprostoru, přičemž se předpokládá, že předměty se pohybují po <a href="/wiki/Geodetika" title="Geodetika">geodetikách</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Externí_odkazy"><span id="Extern.C3.AD_odkazy"></span>Externí odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Riemannova_geometrie&veaction=edit&section=2" title="Editace sekce: Externí odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Riemannova_geometrie&action=edit&section=2" title="Editovat zdrojový kód sekce Externí odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="wd"><span class="sisterproject sisterproject-commons"><span class="sisterproject_image"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons"><img alt="Logo Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></span> <span class="sisterproject_text">Obrázky, zvuky či videa k tématu <span class="sisterproject_text_target"><a href="https://commons.wikimedia.org/wiki/Category:Riemannian_geometry" class="extiw" title="c:Category:Riemannian geometry">Riemannova geometrie</a></span> na <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a></span></span></span><i> </i></li></ul> <table class="plainlinks metadata noprint pahyl" cellpadding="2" style="background: transparent;"> <tbody><tr> <td><figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/Soubor:Wiki_letter_w.svg" class="mw-file-description" title="Pahýl"><img alt="Pahýl" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/40px-Wiki_letter_w.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/60px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/80px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a><figcaption>Pahýl</figcaption></figure> </td> <td><i>Tento článek je příliš stručný nebo <a href="/wiki/Wikipedie:Pah%C3%BDl" title="Wikipedie:Pahýl">postrádá důležité informace</a>.<br />Pomozte Wikipedii tím, že jej vhodně <a class="external text" href="https://cs.wikipedia.org/w/index.php?title=Riemannova_geometrie&action=edit">rozšíříte</a>. 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