CINXE.COM

Manifolds and Differential Geometry - Jeffrey Marc Lee - Google Books

<!DOCTYPE html><html><head><title>Manifolds and Differential Geometry - Jeffrey Marc Lee - Google Books</title><link rel="stylesheet" href="/books/css/_4f54b7ece244bea45b37a7418cb9cf10/kl_viewport_kennedy_full_bundle.css" type="text/css" /><link rel="stylesheet"href="https://fonts.googleapis.com/css2?family=Product+Sans:wght@400"><script src="/books/javascript/v2_4f54b7ece244bea45b37a7418cb9cf10__en.js"></script><script>_OC_Hooks = ["_OC_Page", "_OC_SearchReload", "_OC_TocReload", "_OC_EmptyFunc", "_OC_SearchPage", "_OC_QuotePage" ];for (var _OC_i = 0; _OC_i < _OC_Hooks.length; _OC_i++) {eval("var " + _OC_Hooks[_OC_i] + ";");}function _OC_InitHooks () {for (var i = 0; i < _OC_Hooks.length; i++) {var func = arguments[i];eval( _OC_Hooks[i] + " = func;");}}</script><link rel="canonical" href="https://books.google.com/books/about/Manifolds_and_Differential_Geometry.html?id=QqHdHy9WsEoC"/><meta property="og:url" content="https://books.google.com/books/about/Manifolds_and_Differential_Geometry.html?id=QqHdHy9WsEoC"/><meta name="title" content="Manifolds and Differential Geometry"/><meta name="description" content="&quot;Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell&#39;s equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry.&quot;--Publisher&#39;s website."/><meta property="og:title" content="Manifolds and Differential Geometry"/><meta property="og:type" content="book"/><meta property="og:site_name" content="Google Books"/><meta property="og:image" content="https://books.google.com.sg/books/content?id=QqHdHy9WsEoC&amp;printsec=frontcover&amp;img=1&amp;zoom=1&amp;edge=curl&amp;imgtk=AFLRE73XQecClQuS9tDp7UpfG-CvNYVK-SELuyAVWvu_IzAE2UWNA2WaE1nxHLFbVii7L_uiNVITYPiQJLl70ypqjCo_iXbNLD74F-cxHepRJYt8SnaquH6L1DUrtD1MA8Ek1790Q4uI"/><link rel="image_src" href="https://books.google.com.sg/books/content?id=QqHdHy9WsEoC&amp;printsec=frontcover&amp;img=1&amp;zoom=1&amp;edge=curl&amp;imgtk=AFLRE73XQecClQuS9tDp7UpfG-CvNYVK-SELuyAVWvu_IzAE2UWNA2WaE1nxHLFbVii7L_uiNVITYPiQJLl70ypqjCo_iXbNLD74F-cxHepRJYt8SnaquH6L1DUrtD1MA8Ek1790Q4uI"/><script></script><style>#gbar,#guser{font-size:13px;padding-top:1px !important;}#gbar{height:22px}#guser{padding-bottom:7px !important;text-align:right}.gbh,.gbd{border-top:1px solid #c9d7f1;font-size:1px}.gbh{height:0;position:absolute;top:24px;width:100%}@media all{.gb1{height:22px;margin-right:.5em;vertical-align:top}#gbar{float:left}}a.gb1,a.gb4{text-decoration:underline !important}a.gb1,a.gb4{color:#00c !important}.gbi .gb4{color:#dd8e27 !important}.gbf .gb4{color:#900 !important} #gbar { padding:.3em .6em !important;}</style></head><body class=""><div id=gbar><nobr><a target=_blank class=gb1 href="https://www.google.com.sg/search?tab=pw">Search</a> <a target=_blank class=gb1 href="https://www.google.com.sg/imghp?hl=en&tab=pi">Images</a> <a target=_blank class=gb1 href="https://maps.google.com.sg/maps?hl=en&tab=pl">Maps</a> <a target=_blank class=gb1 href="https://play.google.com/?hl=en&tab=p8">Play</a> <a target=_blank class=gb1 href="https://www.youtube.com/?tab=p1">YouTube</a> <a target=_blank class=gb1 href="https://news.google.com/?tab=pn">News</a> <a target=_blank class=gb1 href="https://mail.google.com/mail/?tab=pm">Gmail</a> <a target=_blank class=gb1 href="https://drive.google.com/?tab=po">Drive</a> <a target=_blank class=gb1 style="text-decoration:none" href="https://www.google.com.sg/intl/en/about/products?tab=ph"><u>More</u> &raquo;</a></nobr></div><div id=guser width=100%><nobr><span id=gbn class=gbi></span><span id=gbf class=gbf></span><span id=gbe></span><a target=_top id=gb_70 href="https://www.google.com/accounts/Login?service=print&continue=https://books.google.com.sg/books%3Fid%3DQqHdHy9WsEoC%26pg%3DPA7%26redir_esc%3Dy%26hl%3Den&hl=en&ec=GAZACg" class=gb4>Sign in</a></nobr></div><div class=gbh style=left:0></div><div class=gbh style=right:0></div><div role="alert" style="position: absolute; left: 0; right: 0;"><a href="https://books.google.com.sg/books?id=QqHdHy9WsEoC&amp;pg=PA7&amp;redir_esc=y&amp;hl=en&amp;output=html_text" title="Screen reader users: click this link for accessible mode. Accessible mode has the same essential features but works better with your reader."><img border="0" src="//www.google.com/images/cleardot.gif"alt="Screen reader users: click this link for accessible mode. Accessible mode has the same essential features but works better with your reader."></a></div><div class="kd-appbar"><h2 class="kd-appname"><a href="/books">Books</a></h2><div class="kd-buttonbar left" id="left-toolbar-buttons"><a id="appbar-view-print-sample-link" href="https://books.google.com.sg/books?id=QqHdHy9WsEoC&amp;printsec=frontcover&amp;source=gbs_vpt_read"></a><a id="appbar-view-ebook-sample-link" href="https://play.google.com/books/reader?id=QqHdHy9WsEoC&amp;source=gbs_vpt_read"></a><a id="appbar-patents-prior-art-finder-link" href=""></a><a id="appbar-patents-discuss-this-link" href="" data-is-grant=""></a><a id="appbar-read-patent-link" href=""></a><a id="appbar-download-pdf-link" href=""></a></div><div class="kd-buttonbar right" id="right-toolbar-buttons"></div></div><div style="display: none"><ol id="ofe-gear-menu-contents" class="gbmcc"><li class="gbe gbmtc"><a class="gbmt goog-menuitem-content" id="" href="https://www.google.com/accounts/Login?service=print&amp;continue=https://books.google.com.sg/books%3Fop%3Dlibrary&amp;hl=en">My library</a></li><li class="gbe gbmtc"><a class="gbmt goog-menuitem-content" id="" href="http://books.google.com.sg/support/topic/4359341?hl=en-SG">Help</a></li><li class="gbe gbmtc"><a class="gbmt goog-menuitem-content" id="" href="https://books.google.com.sg/advanced_book_search">Advanced Book Search</a></li></ol></div><div id="volume-main"><div id="volume-left"><div id=menu_container ><div id="menu_scroll_wrapper"><div id="menu_scroll" role="navigation"><div id="gb-get-book-container"><a href="https://play.google.com/store/books/details?id=QqHdHy9WsEoC&amp;rdid=book-QqHdHy9WsEoC&amp;rdot=1&amp;source=gbs_vpt_read&amp;pcampaignid=books_booksearch_viewport" id="gb-get-book-content">Buy eBook - SGD聽99.95</a></div><p id="gb-buy-options-trigger" class="gb-buy-options-link">Get this book in print</p><h3 class=about_title><a name="buy_anchor"></a></h3><div id=buy class=about_content><div id=buy_v><ul style="list-style-type: none; padding-left: 0; margin: 0;"><li><a style="white-space:normal" href="http://www.ams.org/bookstore-getitem/item=GSM/107" dir=ltr onMouseOver="this.href='http://www.ams.org/bookstore-getitem/item\x3dGSM/107';return false" onMouseDown="this.href='/url?client\x3dca-print-ams\x26format\x3dgoogleprint\x26num\x3d0\x26id\x3dQqHdHy9WsEoC\x26q\x3dhttp://www.ams.org/bookstore-getitem/item%3DGSM/107\x26usg\x3dAOvVaw05Wst4fE6qFWqiwjfHYouU\x26source\x3dgbs_buy_r';return true"><span dir=ltr>AMS Bookstore</span></a></li><li><a style="white-space:normal" href="http://www.amazon.com/gp/search?index=books&amp;linkCode=qs&amp;keywords=9780821848159" dir=ltr onMouseOver="this.href='http://www.amazon.com/gp/search?index\x3dbooks\x26linkCode\x3dqs\x26keywords\x3d9780821848159';return false" onMouseDown="this.href='/url?client\x3dca-print-ams\x26format\x3dgoogleprint\x26num\x3d0\x26id\x3dQqHdHy9WsEoC\x26q\x3dhttp://www.amazon.com/gp/search%3Findex%3Dbooks%26linkCode%3Dqs%26keywords%3D9780821848159\x26usg\x3dAOvVaw1nlIEqkyXxvKCeiQHPZKzH\x26source\x3dgbs_buy_r';return true"><span dir=ltr>Amazon.com</span></a></li><li><a style="white-space:normal" href="http://www.mphonline.com/books/nsearch.aspx?do=detail&amp;pcode=9780821848159" dir=ltr onMouseOver="this.href='http://www.mphonline.com/books/nsearch.aspx?do\x3ddetail\x26pcode\x3d9780821848159';return false" onMouseDown="this.href='/url?client\x3dca-print-ams\x26format\x3dgoogleprint\x26num\x3d0\x26id\x3dQqHdHy9WsEoC\x26q\x3dhttp://www.mphonline.com/books/nsearch.aspx%3Fdo%3Ddetail%26pcode%3D9780821848159\x26usg\x3dAOvVaw3dimKZR9mBqF72Z7s2kSVP\x26source\x3dgbs_buy_r';return true"><span dir=ltr>MPH</span></a></li><li><a style="white-space:normal" href="https://www.popular.com.sg/catalogsearch/result/?q=9780821848159" dir=ltr onMouseOver="this.href='https://www.popular.com.sg/catalogsearch/result/?q\x3d9780821848159';return false" onMouseDown="this.href='/url?client\x3dca-print-ams\x26format\x3dgoogleprint\x26num\x3d0\x26id\x3dQqHdHy9WsEoC\x26q\x3dhttps://www.popular.com.sg/catalogsearch/result/%3Fq%3D9780821848159\x26usg\x3dAOvVaw3mUlzIylGOw8Tx8YVJAc6M\x26source\x3dgbs_buy_r';return true"><span dir=ltr>Popular</span></a></li><li><hr style="margin-right: 20%; color: #666;"></li><li><a style="white-space:normal" href="https://books.google.com.sg/url?id=QqHdHy9WsEoC&amp;pg=PA7&amp;q=http://www.worldcat.org/oclc/1025709091&amp;clientid=librarylink&amp;usg=AOvVaw1btwe-BQDPIkHC8HAPV8WA&amp;source=gbs_buy_r"><span dir=ltr>Find in a library</span></a></li><li><a class="secondary" style="white-space:normal" href="https://books.google.com.sg/books?id=QqHdHy9WsEoC&amp;sitesec=buy&amp;source=gbs_buy_r" id="get-all-sellers-link"><span dir=ltr>All sellers</span>&nbsp;&raquo;</a></li></ul></div></div><div class=menu id=menu><div class="menu_content" style="margin-bottom:6px"><div style="margin-bottom:4px"><div class="sidebarnav"><table border="0" cellpadding="0" cellspacing="0"><tr><td><div class="sidebarcover"><a href="https://books.google.com.sg/books?id=QqHdHy9WsEoC&amp;printsec=frontcover" onclick="_OC_Page('PP1',this.href); return false;"><img src="https://books.google.com.sg/books/content?id=QqHdHy9WsEoC&printsec=frontcover&img=1&zoom=5&edge=curl&imgtk=AFLRE71Z5do9NIIOaCL6T-3nnZ3wWt4AVpJxBD1L6UDo1YfFTj0GjCJFl3gaHNa8lDCBP8AbsRjYl8bBki0XbJ1MUp5l97N-nL2xFzJF3JHML70hNUAGFzdMpeTKRPDm3O7vtE-VXPUC" alt="Front Cover" title="Front Cover" height=80 border=1 id=summary-frontcover ></a></div></td><td></td></tr></table></div><div style="clear:both"></div></div><div id="volume-info-sidebar"><h1 class="gb-volume-title" dir=ltr>Manifolds and Differential Geometry</h1><span class="addmd">By Jeffrey Marc Lee</span></div><div style="margin-bottom:3px"><form action=/books id=search_form style="margin:0px;padding:0px;" method=get> <input type=hidden name="redir_esc" value="y"><input type=hidden name="id" value="QqHdHy9WsEoC"><table cellpadding=0 cellspacing=0 class="swv-table"><tr><td class="swv-td-search"><span><input id=search_form_input type=text maxlength=1024 class="text_flat swv-input-search" aria-label="Search in this book" name=q value="" title="Go" accesskey=i></span></td><td class="swv-td-space"><div>&nbsp;</div></td><td><input type=submit value="Go"></td></tr></table><script type="text/javascript">if (window['_OC_autoDir']) {_OC_autoDir('search_form_input');}</script></form></div><div><p><a id="sidebar-atb-link" href="https://books.google.com.sg/books?id=QqHdHy9WsEoC&amp;source=gbs_navlinks_s"><span dir=ltr>About this book</span></a></p></div></div></div><div><div id="navbarContainer" class="gb-navbar"></div><script>_OC_InitNavbar({"child_node":[{"title":"My library","url":"https://books.google.com.sg/books?uid=114584440181414684107\u0026source=gbs_lp_bookshelf_list","id":"my_library","collapsed":true},{"title":"My History","url":"","id":"my_history","collapsed":true}],"highlighted_node_id":""});</script><a href="/intl/en/googlebooks/tos.html" target="_blank">Terms&nbsp;of&nbsp;Service</a><h3 class=about_title><a name="pub_info_anchor"></a></h3><div id=pub_info class=about_content><div id=pub_info_v><table cellspacing=0><tr><td><a href="https://books.google.com.sg/url?id=QqHdHy9WsEoC&amp;pg=PA7&amp;q=http://www.ams.org/bookstore&amp;clientid=ca-print-ams&amp;linkid=1&amp;usg=AOvVaw1q84riBerQzeD7iisJ3leq&amp;source=gbs_pub_info_r" style="text-decoration:none"><img width=175 height=35 border=0 src="https://pagead2.googlesyndication.com/pagead/imgad?id=CMz65v2v1LDEugEQvgEYJjIIEXz9vzia33I" alt="American Mathematical Soc."></a><tr><td style="font-size:84.6%;color:#666666">Pages displayed by permission of <a class=link_aux href="https://books.google.com.sg/url?id=QqHdHy9WsEoC&pg=PA7&q=http://www.ams.org/bookstore&clientid=ca-print-ams&linkid=1&usg=AOvVaw1q84riBerQzeD7iisJ3leq&source=gbs_pub_info_r">American Mathematical Soc.</a>.&nbsp;<a style="color:#7777cc;white-space:normal" href="https://books.google.com.sg/books?id=QqHdHy9WsEoC&amp;printsec=copyright&amp;source=gbs_pub_info_r">Copyright</a>.&nbsp;</table></div></div></div></div></div></div></div><div id="volume-center"><div id="scroll_atb" role="main"><div id="toolbar_container"><div style="float:left;white-space:nowrap"><table cellpadding=0 cellspacing=0><tr><td id="l_toolbar"></td><td class=toolbar-pc-cell><table cellpadding=0 cellspacing=0><tr><td class=no-jump-cell align=right><span id=page_label style="margin-right:.5em">Page 7</span></td><td class=arrow style="padding-right:2px"><a href="https://books.google.com.sg/books?id=QqHdHy9WsEoC&amp;pg=PA6&amp;lpg=PA7&amp;focus=viewport" onclick="_OC_EmptyFunc(this.href); return false;"><div class=pagination><div id=prev_btn alt="Previous Page" title="Previous Page" class="SPRITE_pagination_v2_left"></div></div></a></td><td class=arrow><a href="https://books.google.com.sg/books?id=QqHdHy9WsEoC&amp;pg=PA8&amp;lpg=PA7&amp;focus=viewport" onclick="_OC_EmptyFunc(this.href); return false;"><div class=pagination><div id=next_btn alt="Next Page" title="Next Page" class="SPRITE_pagination_v2_right"></div></div></a></td></tr></table></td><td>&nbsp;&nbsp;</td><td id=view_toolbar></td><td id=view_new></td></tr></table></div><div style="float:right"><table cellpadding=0 cellspacing=0><tr><td></td><td id="r_toolbar" style="white-space:nowrap"></td></tr></table></div><div style="clear:both"></div></div><div id="search_bar"></div><div class="gback"><div id="viewport" class="viewport" tabindex="0"><a name="page" accesskey="c"></a><table class="viewport-table" id="container" align="center" cellpadding="0" cellspacing="0"><tr><td valign="top" align="center"><noscript><style type=text/css media=print> .html_page_image{display:none;} .viewport div img {display:none;} </style><div style="height:812px;width:575px;position:relative;margin-bottom:4px"><style type=text/css>.html_page_image { background-image:url("https://books.google.com.sg/books/content?id=QqHdHy9WsEoC&pg=PA7&img=1&zoom=3&hl=en&sig=ACfU3U1pgRQoGmtqFx8Bf_7DqIGm7a3lrw"); width:575px;height:812px; top:0px;left:0px;position:relative}</style><div class=html_page_image><a href="https://books.google.com.sg/books?id=QqHdHy9WsEoC&amp;pg=PA8&amp;lpg=PA7&amp;focus=viewport" style="outline:none"><img class=html_page_secure_image src="//www.google.com/images/cleardot.gif" height=812 width=575 border=0 alt="Next Page" title="Next Page"></a></div></div></noscript></td></tr></table></div></div><script>_OC_addFlags({Host:"https://books.google.com.sg/", IsBooksUnifiedLeftNavEnabled:1, IsBooksRentalEnabled:1, IsBrowsingHistoryEnabled:1, IsZipitFolderCollectionEnabled:1});_OC_Run({"page":[{"pid":"PP1","flags":32,"order":0},{"pid":"PR4","order":4,"title":"iv"},{"pid":"PR5","order":5,"title":"v"},{"pid":"PR6","order":6,"title":"vi"},{"pid":"PR7","order":7,"title":"vii"},{"pid":"PR8","order":8,"title":"viii"},{"pid":"PR9","order":9,"title":"ix"},{"pid":"PR10","order":10,"title":"x"},{"pid":"PR11","order":11,"title":"xi"},{"pid":"PR12","order":12,"title":"xii"},{"pid":"PR13","order":13,"title":"xiii"},{"pid":"PR14","order":14,"title":"xiv"},{"pid":"PA1","order":15,"title":"1"},{"pid":"PA2","order":16,"title":"2"},{"pid":"PA3","order":17,"title":"3"},{"pid":"PA4","order":18,"title":"4"},{"pid":"PA5","order":19,"title":"5"},{"pid":"PA6","order":20,"title":"6"},{"pid":"PA7","order":21,"title":"7"},{"pid":"PA8","order":22,"title":"8"},{"pid":"PA9","order":23,"title":"9"},{"pid":"PA10","order":24,"title":"10"},{"pid":"PA11","order":25,"title":"11"},{"pid":"PA12","order":26,"title":"12"},{"pid":"PA13","order":27,"title":"13"},{"pid":"PA14","order":28,"title":"14"},{"pid":"PA15","order":29,"title":"15"},{"pid":"PA16","order":30,"title":"16"},{"pid":"PA17","order":31,"title":"17"},{"pid":"PA18","order":32,"title":"18"},{"pid":"PA19","order":33,"title":"19"},{"pid":"PA20","order":34,"title":"20"},{"pid":"PA21","order":35,"title":"21"},{"pid":"PA22","order":36,"title":"22"},{"pid":"PA23","order":37,"title":"23"},{"pid":"PA24","order":38,"title":"24"},{"pid":"PA25","order":39,"title":"25"},{"pid":"PA26","order":40,"title":"26"},{"pid":"PA27","order":41,"title":"27"},{"pid":"PA28","order":42,"title":"28"},{"pid":"PA29","order":43,"title":"29"},{"pid":"PA30","order":44,"title":"30"},{"pid":"PA31","order":45,"title":"31"},{"pid":"PA32","order":46,"title":"32"},{"pid":"PA33","order":47,"title":"33"},{"pid":"PA34","order":48,"title":"34"},{"pid":"PA35","order":49,"title":"35"},{"pid":"PA36","order":50,"title":"36"},{"pid":"PA37","order":51,"title":"37"},{"pid":"PA38","order":52,"title":"38"},{"pid":"PA39","order":53,"title":"39"},{"pid":"PA40","order":54,"title":"40"},{"pid":"PA41","order":55,"title":"41"},{"pid":"PA42","order":56,"title":"42"},{"pid":"PA43","order":57,"title":"43"},{"pid":"PA44","order":58,"title":"44"},{"pid":"PA45","order":59,"title":"45"},{"pid":"PA46","order":60,"title":"46"},{"pid":"PA47","order":61,"title":"47"},{"pid":"PA48","order":62,"title":"48"},{"pid":"PA49","order":63,"title":"49"},{"pid":"PA50","order":64,"title":"50"},{"pid":"PA51","order":65,"title":"51"},{"pid":"PA52","order":66,"title":"52"},{"pid":"PA53","order":67,"title":"53"},{"pid":"PA54","order":68,"title":"54"},{"pid":"PA55","order":69,"title":"55"},{"pid":"PA56","order":70,"title":"56"},{"pid":"PA57","order":71,"title":"57"},{"pid":"PA58","order":72,"title":"58"},{"pid":"PA59","order":73,"title":"59"},{"pid":"PA60","order":74,"title":"60"},{"pid":"PA61","order":75,"title":"61"},{"pid":"PA62","order":76,"title":"62"},{"pid":"PA63","order":77,"title":"63"},{"pid":"PA64","order":78,"title":"64"},{"pid":"PA65","order":79,"title":"65"},{"pid":"PA66","order":80,"title":"66"},{"pid":"PA67","order":81,"title":"67"},{"pid":"PA68","order":82,"title":"68"},{"pid":"PA69","order":83,"title":"69"},{"pid":"PA70","order":84,"title":"70"},{"pid":"PA71","order":85,"title":"71"},{"pid":"PA72","order":86,"title":"72"},{"pid":"PA73","order":87,"title":"73"},{"pid":"PA74","order":88,"title":"74"},{"pid":"PA75","order":89,"title":"75"},{"pid":"PA76","order":90,"title":"76"},{"pid":"PA77","order":91,"title":"77"},{"pid":"PA78","order":92,"title":"78"},{"pid":"PA79","order":93,"title":"79"},{"pid":"PA80","order":94,"title":"80"},{"pid":"PA81","order":95,"title":"81"},{"pid":"PA82","order":96,"title":"82"},{"pid":"PA83","order":97,"title":"83"},{"pid":"PA84","order":98,"title":"84"},{"pid":"PA85","order":99,"title":"85"},{"pid":"PA86","order":100,"title":"86"},{"pid":"PA87","order":101,"title":"87"},{"pid":"PA88","order":102,"title":"88"},{"pid":"PA89","order":103,"title":"89"},{"pid":"PA90","order":104,"title":"90"},{"pid":"PA91","order":105,"title":"91"},{"pid":"PA92","order":106,"title":"92"},{"pid":"PA93","order":107,"title":"93"},{"pid":"PA94","order":108,"title":"94"},{"pid":"PA95","order":109,"title":"95"},{"pid":"PA96","order":110,"title":"96"},{"pid":"PA97","order":111,"title":"97"},{"pid":"PA98","order":112,"title":"98"},{"pid":"PA99","order":113,"title":"99"},{"pid":"PA100","order":114,"title":"100"},{"pid":"PA101","order":115,"title":"101"},{"pid":"PA102","order":116,"title":"102"},{"pid":"PA103","order":117,"title":"103"},{"pid":"PA104","order":118,"title":"104"},{"pid":"PA105","order":119,"title":"105"},{"pid":"PA106","order":120,"title":"106"},{"pid":"PA107","order":121,"title":"107"},{"pid":"PA108","order":122,"title":"108"},{"pid":"PA109","order":123,"title":"109"},{"pid":"PA110","order":124,"title":"110"},{"pid":"PA111","order":125,"title":"111"},{"pid":"PA112","order":126,"title":"112"},{"pid":"PA113","order":127,"title":"113"},{"pid":"PA114","order":128,"title":"114"},{"pid":"PA115","order":129,"title":"115"},{"pid":"PA116","order":130,"title":"116"},{"pid":"PA117","order":131,"title":"117"},{"pid":"PA118","order":132,"title":"118"},{"pid":"PA119","order":133,"title":"119"},{"pid":"PA120","order":134,"title":"120"},{"pid":"PA121","order":135,"title":"121"},{"pid":"PA122","order":136,"title":"122"},{"pid":"PA123","order":137,"title":"123"},{"pid":"PA124","order":138,"title":"124"},{"pid":"PA125","order":139,"title":"125"},{"pid":"PA126","order":140,"title":"126"},{"pid":"PA127","order":141,"title":"127"},{"pid":"PA128","order":142,"title":"128"},{"pid":"PA129","order":143,"title":"129"},{"pid":"PA130","order":144,"title":"130"},{"pid":"PA131","order":145,"title":"131"},{"pid":"PA132","order":146,"title":"132"},{"pid":"PA133","order":147,"title":"133"},{"pid":"PA134","order":148,"title":"134"},{"pid":"PA135","order":149,"title":"135"},{"pid":"PA136","order":150,"title":"136"},{"pid":"PA137","order":151,"title":"137"},{"pid":"PA138","order":152,"title":"138"},{"pid":"PA139","order":153,"title":"139"},{"pid":"PA140","order":154,"title":"140"},{"pid":"PA141","order":155,"title":"141"},{"pid":"PA142","order":156,"title":"142"},{"pid":"PA143","order":157,"title":"143"},{"pid":"PA144","order":158,"title":"144"},{"pid":"PA145","order":159,"title":"145"},{"pid":"PA146","order":160,"title":"146"},{"pid":"PA147","order":161,"title":"147"},{"pid":"PA148","order":162,"title":"148"},{"pid":"PA149","order":163,"title":"149"},{"pid":"PA150","order":164,"title":"150"},{"pid":"PA151","order":165,"title":"151"},{"pid":"PA152","order":166,"title":"152"},{"pid":"PA153","order":167,"title":"153"},{"pid":"PA154","order":168,"title":"154"},{"pid":"PA155","order":169,"title":"155"},{"pid":"PA156","order":170,"title":"156"},{"pid":"PA157","order":171,"title":"157"},{"pid":"PA158","order":172,"title":"158"},{"pid":"PA159","order":173,"title":"159"},{"pid":"PA160","order":174,"title":"160"},{"pid":"PA161","order":175,"title":"161"},{"pid":"PA162","order":176,"title":"162"},{"pid":"PA163","order":177,"title":"163"},{"pid":"PA164","order":178,"title":"164"},{"pid":"PA165","order":179,"title":"165"},{"pid":"PA166","order":180,"title":"166"},{"pid":"PA167","order":181,"title":"167"},{"pid":"PA168","order":182,"title":"168"},{"pid":"PA169","order":183,"title":"169"},{"pid":"PA170","order":184,"title":"170"},{"pid":"PA171","order":185,"title":"171"},{"pid":"PA172","order":186,"title":"172"},{"pid":"PA173","order":187,"title":"173"},{"pid":"PA174","order":188,"title":"174"},{"pid":"PA175","order":189,"title":"175"},{"pid":"PA176","order":190,"title":"176"},{"pid":"PA177","order":191,"title":"177"},{"pid":"PA178","order":192,"title":"178"},{"pid":"PA179","order":193,"title":"179"},{"pid":"PA180","order":194,"title":"180"},{"pid":"PA181","order":195,"title":"181"},{"pid":"PA182","order":196,"title":"182"},{"pid":"PA183","order":197,"title":"183"},{"pid":"PA184","order":198,"title":"184"},{"pid":"PA185","order":199,"title":"185"},{"pid":"PA186","order":200,"title":"186"},{"pid":"PA187","order":201,"title":"187"},{"pid":"PA188","order":202,"title":"188"},{"pid":"PA189","order":203,"title":"189"},{"pid":"PA190","order":204,"title":"190"},{"pid":"PA191","order":205,"title":"191"},{"pid":"PA192","order":206,"title":"192"},{"pid":"PA193","order":207,"title":"193"},{"pid":"PA194","order":208,"title":"194"},{"pid":"PA195","order":209,"title":"195"},{"pid":"PA196","order":210,"title":"196"},{"pid":"PA197","order":211,"title":"197"},{"pid":"PA198","order":212,"title":"198"},{"pid":"PA199","order":213,"title":"199"},{"pid":"PA200","order":214,"title":"200"},{"pid":"PA201","order":215,"title":"201"},{"pid":"PA202","order":216,"title":"202"},{"pid":"PA203","order":217,"title":"203"},{"pid":"PA204","order":218,"title":"204"},{"pid":"PA205","order":219,"title":"205"},{"pid":"PA206","order":220,"title":"206"},{"pid":"PA207","order":221,"title":"207"},{"pid":"PA208","order":222,"title":"208"},{"pid":"PA209","order":223,"title":"209"},{"pid":"PA210","order":224,"title":"210"},{"pid":"PA211","order":225,"title":"211"},{"pid":"PA212","order":226,"title":"212"},{"pid":"PA213","order":227,"title":"213"},{"pid":"PA214","order":228,"title":"214"},{"pid":"PA215","order":229,"title":"215"},{"pid":"PA216","order":230,"title":"216"},{"pid":"PA217","order":231,"title":"217"},{"pid":"PA218","order":232,"title":"218"},{"pid":"PA219","order":233,"title":"219"},{"pid":"PA220","order":234,"title":"220"},{"pid":"PA221","order":235,"title":"221"},{"pid":"PA222","order":236,"title":"222"},{"pid":"PA223","order":237,"title":"223"},{"pid":"PA224","order":238,"title":"224"},{"pid":"PA225","order":239,"title":"225"},{"pid":"PA226","order":240,"title":"226"},{"pid":"PA227","order":241,"title":"227"},{"pid":"PA228","order":242,"title":"228"},{"pid":"PA229","order":243,"title":"229"},{"pid":"PA230","order":244,"title":"230"},{"pid":"PA231","order":245,"title":"231"},{"pid":"PA232","order":246,"title":"232"},{"pid":"PA233","order":247,"title":"233"},{"pid":"PA234","order":248,"title":"234"},{"pid":"PA235","order":249,"title":"235"},{"pid":"PA236","order":250,"title":"236"},{"pid":"PA237","order":251,"title":"237"},{"pid":"PA238","order":252,"title":"238"},{"pid":"PA239","order":253,"title":"239"},{"pid":"PA240","order":254,"title":"240"},{"pid":"PA241","order":255,"title":"241"},{"pid":"PA242","order":256,"title":"242"},{"pid":"PA243","order":257,"title":"243"},{"pid":"PA244","order":258,"title":"244"},{"pid":"PA245","order":259,"title":"245"},{"pid":"PA246","order":260,"title":"246"},{"pid":"PA247","order":261,"title":"247"},{"pid":"PA248","order":262,"title":"248"},{"pid":"PA249","order":263,"title":"249"},{"pid":"PA250","order":264,"title":"250"},{"pid":"PA251","order":265,"title":"251"},{"pid":"PA252","order":266,"title":"252"},{"pid":"PA253","order":267,"title":"253"},{"pid":"PA254","order":268,"title":"254"},{"pid":"PA255","order":269,"title":"255"},{"pid":"PA256","order":270,"title":"256"},{"pid":"PA257","order":271,"title":"257"},{"pid":"PA258","order":272,"title":"258"},{"pid":"PA259","order":273,"title":"259"},{"pid":"PA260","order":274,"title":"260"},{"pid":"PA261","order":275,"title":"261"},{"pid":"PA262","order":276,"title":"262"},{"pid":"PA263","order":277,"title":"263"},{"pid":"PA264","order":278,"title":"264"},{"pid":"PA265","order":279,"title":"265"},{"pid":"PA266","order":280,"title":"266"},{"pid":"PA267","order":281,"title":"267"},{"pid":"PA268","order":282,"title":"268"},{"pid":"PA269","order":283,"title":"269"},{"pid":"PA270","order":284,"title":"270"},{"pid":"PA271","order":285,"title":"271"},{"pid":"PA272","order":286,"title":"272"},{"pid":"PA273","order":287,"title":"273"},{"pid":"PA274","order":288,"title":"274"},{"pid":"PA275","order":289,"title":"275"},{"pid":"PA276","order":290,"title":"276"},{"pid":"PA277","order":291,"title":"277"},{"pid":"PA278","order":292,"title":"278"},{"pid":"PA279","order":293,"title":"279"},{"pid":"PA280","order":294,"title":"280"},{"pid":"PA281","order":295,"title":"281"},{"pid":"PA282","order":296,"title":"282"},{"pid":"PA283","order":297,"title":"283"},{"pid":"PA284","order":298,"title":"284"},{"pid":"PA285","order":299,"title":"285"},{"pid":"PA286","order":300,"title":"286"},{"pid":"PA287","order":301,"title":"287"},{"pid":"PA288","order":302,"title":"288"},{"pid":"PA289","order":303,"title":"289"},{"pid":"PA290","order":304,"title":"290"},{"pid":"PA291","order":305,"title":"291"},{"pid":"PA292","order":306,"title":"292"},{"pid":"PA293","order":307,"title":"293"},{"pid":"PA294","order":308,"title":"294"},{"pid":"PA295","order":309,"title":"295"},{"pid":"PA296","order":310,"title":"296"},{"pid":"PA297","order":311,"title":"297"},{"pid":"PA298","order":312,"title":"298"},{"pid":"PA299","order":313,"title":"299"},{"pid":"PA300","order":314,"title":"300"},{"pid":"PA301","order":315,"title":"301"},{"pid":"PA302","order":316,"title":"302"},{"pid":"PA303","order":317,"title":"303"},{"pid":"PA304","order":318,"title":"304"},{"pid":"PA305","order":319,"title":"305"},{"pid":"PA306","order":320,"title":"306"},{"pid":"PA307","order":321,"title":"307"},{"pid":"PA308","order":322,"title":"308"},{"pid":"PA309","order":323,"title":"309"},{"pid":"PA310","order":324,"title":"310"},{"pid":"PA311","order":325,"title":"311"},{"pid":"PA312","order":326,"title":"312"},{"pid":"PA313","order":327,"title":"313"},{"pid":"PA314","order":328,"title":"314"},{"pid":"PA315","order":329,"title":"315"},{"pid":"PA316","order":330,"title":"316"},{"pid":"PA317","order":331,"title":"317"},{"pid":"PA318","order":332,"title":"318"},{"pid":"PA319","order":333,"title":"319"},{"pid":"PA320","order":334,"title":"320"},{"pid":"PA321","order":335,"title":"321"},{"pid":"PA322","order":336,"title":"322"},{"pid":"PA323","order":337,"title":"323"},{"pid":"PA324","order":338,"title":"324"},{"pid":"PA325","order":339,"title":"325"},{"pid":"PA326","order":340,"title":"326"},{"pid":"PA327","order":341,"title":"327"},{"pid":"PA328","order":342,"title":"328"},{"pid":"PA329","order":343,"title":"329"},{"pid":"PA330","order":344,"title":"330"},{"pid":"PA331","order":345,"title":"331"},{"pid":"PA332","order":346,"title":"332"},{"pid":"PA333","order":347,"title":"333"},{"pid":"PA334","order":348,"title":"334"},{"pid":"PA335","order":349,"title":"335"},{"pid":"PA336","order":350,"title":"336"},{"pid":"PA337","order":351,"title":"337"},{"pid":"PA338","order":352,"title":"338"},{"pid":"PA341","order":355,"title":"341"},{"pid":"PA342","order":356,"title":"342"},{"pid":"PA343","order":357,"title":"343"},{"pid":"PA345","order":359,"title":"345"},{"pid":"PA346","order":360,"title":"346"},{"pid":"PA347","order":361,"title":"347"},{"pid":"PA348","order":362,"title":"348"},{"pid":"PA349","order":363,"title":"349"},{"pid":"PA350","order":364,"title":"350"},{"pid":"PA351","order":365,"title":"351"},{"pid":"PA352","order":366,"title":"352"},{"pid":"PA353","order":367,"title":"353"},{"pid":"PA356","order":370,"title":"356"},{"pid":"PA357","order":371,"title":"357"},{"pid":"PA360","order":374,"title":"360"},{"pid":"PA361","order":375,"title":"361"},{"pid":"PA364","order":378,"title":"364"},{"pid":"PA365","order":379,"title":"365"},{"pid":"PA366","order":380,"title":"366"},{"pid":"PA368","order":382,"title":"368"},{"pid":"PA373","order":387,"title":"373"},{"pid":"PA375","order":389,"title":"375"},{"pid":"PA376","order":390,"title":"376"},{"pid":"PA377","order":391,"title":"377"},{"pid":"PA380","order":394,"title":"380"},{"pid":"PA382","order":396,"title":"382"},{"pid":"PA384","order":398,"title":"384"},{"pid":"PA388","order":402,"title":"388"},{"pid":"PA389","order":403,"title":"389"},{"pid":"PA390","order":404,"title":"390"},{"pid":"PA391","order":405,"title":"391"},{"pid":"PA392","order":406,"title":"392"},{"pid":"PA393","order":407,"title":"393"},{"pid":"PA394","order":408,"title":"394"},{"pid":"PA395","order":409,"title":"395"},{"pid":"PA397","order":411,"title":"397"},{"pid":"PA398","order":412,"title":"398"},{"pid":"PA399","order":413,"title":"399"},{"pid":"PA400","order":414,"title":"400"},{"pid":"PA401","order":415,"title":"401"},{"pid":"PA402","order":416,"title":"402"},{"pid":"PA405","order":419,"title":"405"},{"pid":"PA406","order":420,"title":"406"},{"pid":"PA409","order":423,"title":"409"},{"pid":"PA410","order":424,"title":"410"},{"pid":"PA411","order":425,"title":"411"},{"pid":"PA413","order":427,"title":"413"},{"pid":"PA414","order":428,"title":"414"},{"pid":"PA416","order":430,"title":"416"},{"pid":"PA417","order":431,"title":"417"},{"pid":"PA421","order":435,"title":"421"},{"pid":"PA423","order":437,"title":"423"},{"pid":"PA424","order":438,"title":"424"},{"pid":"PA426","order":440,"title":"426"},{"pid":"PA428","order":442,"title":"428"},{"pid":"PA429","order":443,"title":"429"},{"pid":"PA430","order":444,"title":"430"},{"pid":"PA434","order":448,"title":"434"},{"pid":"PA436","order":450,"title":"436"},{"pid":"PA438","order":452,"title":"438"},{"pid":"PA440","order":454,"title":"440"},{"pid":"PA441","order":455,"title":"441"},{"pid":"PA442","order":456,"title":"442"},{"pid":"PA443","order":457,"title":"443"},{"pid":"PA444","order":458,"title":"444"},{"pid":"PA447","order":461,"title":"447"},{"pid":"PA448","order":462,"title":"448"},{"pid":"PA449","order":463,"title":"449"},{"pid":"PA450","order":464,"title":"450"},{"pid":"PA451","order":465,"title":"451"},{"pid":"PA454","order":468,"title":"454"},{"pid":"PA455","order":469,"title":"455"},{"pid":"PA456","order":470,"title":"456"},{"pid":"PA458","order":472,"title":"458"},{"pid":"PA459","order":473,"title":"459"},{"pid":"PA460","order":474,"title":"460"},{"pid":"PA461","order":475,"title":"461"},{"pid":"PA462","order":476,"title":"462"},{"pid":"PA463","order":477,"title":"463"},{"pid":"PA464","order":478,"title":"464"},{"pid":"PA465","order":479,"title":"465"},{"pid":"PA466","order":480,"title":"466"},{"pid":"PA467","order":481,"title":"467"},{"pid":"PA468","order":482,"title":"468"},{"pid":"PA469","order":483,"title":"469"},{"pid":"PA470","order":484,"title":"470"},{"pid":"PA473","order":487,"title":"473"},{"pid":"PA474","order":488,"title":"474"},{"pid":"PA475","order":489,"title":"475"},{"pid":"PA476","order":490,"title":"476"},{"pid":"PA477","order":491,"title":"477"},{"pid":"PA478","order":492,"title":"478"},{"pid":"PA481","order":495,"title":"481"},{"pid":"PA482","order":496,"title":"482"},{"pid":"PA484","order":498,"title":"484"},{"pid":"PA485","order":499,"title":"485"},{"pid":"PA487","order":501,"title":"487"},{"pid":"PA488","order":502,"title":"488"},{"pid":"PA491","order":505,"title":"491"},{"pid":"PA492","order":506,"title":"492"},{"pid":"PA494","order":508,"title":"494"},{"pid":"PA496","order":510,"title":"496"},{"pid":"PA497","order":511,"title":"497"},{"pid":"PA498","order":512,"title":"498"},{"pid":"PA499","order":513,"title":"499"},{"pid":"PA500","order":514,"title":"500"},{"pid":"PA501","order":515,"title":"501"},{"pid":"PA502","order":516,"title":"502"},{"pid":"PA503","order":517,"title":"503"},{"pid":"PA504","order":518,"title":"504"},{"pid":"PA505","order":519,"title":"505"},{"pid":"PA506","order":520,"title":"506"},{"pid":"PA508","order":522,"title":"508"},{"pid":"PA509","order":523,"title":"509"},{"pid":"PA510","order":524,"title":"510"},{"pid":"PA511","order":525,"title":"511"},{"pid":"PA513","order":527,"title":"513"},{"pid":"PA514","order":528,"title":"514"},{"pid":"PA517","order":531,"title":"517"},{"pid":"PA518","order":532,"title":"518"},{"pid":"PA524","order":538,"title":"524"},{"pid":"PA525","order":539,"title":"525"},{"pid":"PA526","order":540,"title":"526"},{"pid":"PA527","order":541,"title":"527"},{"pid":"PA530","order":544,"title":"530"},{"pid":"PA531","order":545,"title":"531"},{"pid":"PA532","order":546,"title":"532"},{"pid":"PA533","order":547,"title":"533"},{"pid":"PA534","order":548,"title":"534"},{"pid":"PA535","order":549,"title":"535"},{"pid":"PA536","order":550,"title":"536"},{"pid":"PA539","order":553,"title":"539"},{"pid":"PA543","order":557,"title":"543"},{"pid":"PA545","order":559,"title":"545"},{"pid":"PA546","order":560,"title":"546"},{"pid":"PA547","order":561,"title":"547"},{"pid":"PA548","order":562,"title":"548"},{"pid":"PA549","order":563,"title":"549"},{"pid":"PA550","order":564,"title":"550"},{"pid":"PA551","order":565,"title":"551"},{"pid":"PA553","order":567,"title":"553"},{"pid":"PA555","order":569,"title":"555"},{"pid":"PA556","order":570,"title":"556"},{"pid":"PA557","order":571,"title":"557"},{"pid":"PA558","order":572,"title":"558"},{"pid":"PA559","order":573,"title":"559"},{"pid":"PA561","order":575,"title":"561"},{"pid":"PA562","order":576,"title":"562"},{"pid":"PA563","order":577,"title":"563"},{"pid":"PA564","order":578,"title":"564"},{"pid":"PA565","order":579,"title":"565"},{"pid":"PA566","order":580,"title":"566"},{"pid":"PA568","order":582,"title":"568"},{"pid":"PA569","order":583,"title":"569"},{"pid":"PA570","order":584,"title":"570"},{"pid":"PA571","order":585,"title":"571"},{"pid":"PA572","order":586,"title":"572"},{"pid":"PA574","order":588,"title":"574"},{"pid":"PA576","order":590,"title":"576"},{"pid":"PA577","order":591,"title":"577"},{"pid":"PA579","order":593,"title":"579"},{"pid":"PA580","order":594,"title":"580"},{"pid":"PA583","order":597,"title":"583"},{"pid":"PA584","order":598,"title":"584"},{"pid":"PA585","order":599,"title":"585"},{"pid":"PA587","order":601,"title":"587"},{"pid":"PA589","order":603,"title":"589"},{"pid":"PA590","order":604,"title":"590"},{"pid":"PA591","order":605,"title":"591"},{"pid":"PA592","order":606,"title":"592"},{"pid":"PA593","order":607,"title":"593"},{"pid":"PA596","order":610,"title":"596"},{"pid":"PA597","order":611,"title":"597"},{"pid":"PA598","order":612,"title":"598"},{"pid":"PA599","order":613,"title":"599"},{"pid":"PA602","order":616,"title":"602"},{"pid":"PA604","order":618,"title":"604"},{"pid":"PA608","order":622,"title":"608"},{"pid":"PA610","order":624,"title":"610"},{"pid":"PA612","order":626,"title":"612"},{"pid":"PA614","order":628,"title":"614"},{"pid":"PA615","order":629,"title":"615"},{"pid":"PA616","order":630,"title":"616"},{"pid":"PA617","order":631,"title":"617"},{"pid":"PA618","order":632,"title":"618"},{"pid":"PA620","order":634,"title":"620"},{"pid":"PA624","order":638,"title":"624"},{"pid":"PA625","order":639,"title":"625"},{"pid":"PA626","order":640,"title":"626"},{"pid":"PA628","order":642,"title":"628"},{"pid":"PA629","order":643,"title":"629"},{"pid":"PA634","order":648,"title":"634"},{"pid":"PA636","order":650,"title":"636"},{"pid":"PA637","order":651,"title":"637"},{"pid":"PA638","order":652,"title":"638"},{"pid":"PA643","order":657,"title":"643"},{"pid":"PA644","order":658,"title":"644"},{"pid":"PA646","order":660,"title":"646"},{"pid":"PA648","order":662,"title":"648"},{"pid":"PA649","order":663,"title":"649"},{"pid":"PA650","order":664,"title":"650"},{"pid":"PA651","order":665,"title":"651"},{"pid":"PA658","order":672,"title":"658"},{"pid":"PA659","order":673,"title":"659"},{"pid":"PA661","order":675,"title":"661"},{"pid":"PA662","order":676,"title":"662"},{"pid":"PA663","order":677,"title":"663"},{"pid":"PA664","order":678,"title":"664"},{"pid":"PA666","order":680,"title":"666"},{"pid":"PA667","order":681,"title":"667"},{"pid":"PA668","order":682,"title":"668"},{"pid":"PA669","order":683,"title":"669"},{"pid":"PA670","order":684,"title":"670"},{"pid":"PA671","order":685,"title":"671"},{"pid":"PA672","order":686,"title":"672"},{"pid":"PA673","order":687,"title":"673"},{"pid":"PA674","order":688,"title":"674"}],"prefix":"https://books.google.com.sg/books?id=QqHdHy9WsEoC\u0026lpg=PA7"},{"fullview":false,"page_width":575,"page_height":821,"font_height":12,"first_content_page":15,"disable_twopage":false,"initial_zoom_width_override":685,"show_print_pages_button":false,"title":"Manifolds and Differential Geometry","subtitle":"","attribution":"By Jeffrey Marc Lee","additional_info":{"[JsonBookInfo]":{"BuyLinks":[{"Seller":"AMS Bookstore","Url":"http://www.ams.org/bookstore-getitem/item=GSM/107","TrackingUrl":"/url?client=ca-print-ams\u0026format=googleprint\u0026num=0\u0026id=QqHdHy9WsEoC\u0026q=http://www.ams.org/bookstore-getitem/item%3DGSM/107\u0026usg=AOvVaw05Wst4fE6qFWqiwjfHYouU","IsPublisher":true},{"Seller":"Amazon.com","Url":"http://www.amazon.com/gp/search?index=books\u0026linkCode=qs\u0026keywords=9780821848159","TrackingUrl":"/url?client=ca-print-ams\u0026format=googleprint\u0026num=0\u0026id=QqHdHy9WsEoC\u0026q=http://www.amazon.com/gp/search%3Findex%3Dbooks%26linkCode%3Dqs%26keywords%3D9780821848159\u0026usg=AOvVaw1nlIEqkyXxvKCeiQHPZKzH"},{"Seller":"MPH","Url":"http://www.mphonline.com/books/nsearch.aspx?do=detail\u0026pcode=9780821848159","TrackingUrl":"/url?client=ca-print-ams\u0026format=googleprint\u0026num=0\u0026id=QqHdHy9WsEoC\u0026q=http://www.mphonline.com/books/nsearch.aspx%3Fdo%3Ddetail%26pcode%3D9780821848159\u0026usg=AOvVaw3dimKZR9mBqF72Z7s2kSVP"},{"Seller":"Popular","Url":"https://www.popular.com.sg/catalogsearch/result/?q=9780821848159","TrackingUrl":"/url?client=ca-print-ams\u0026format=googleprint\u0026num=0\u0026id=QqHdHy9WsEoC\u0026q=https://www.popular.com.sg/catalogsearch/result/%3Fq%3D9780821848159\u0026usg=AOvVaw3mUlzIylGOw8Tx8YVJAc6M"}],"AboutUrl":"https://books.google.com.sg/books?id=QqHdHy9WsEoC","PreviewUrl":"https://books.google.com.sg/books?id=QqHdHy9WsEoC","allowed_syndication_flags":{"allow_disabling_chrome":true},"online_access":{"url":"https://play.google.com/store/books/details?id=QqHdHy9WsEoC\u0026rdid=book-QqHdHy9WsEoC\u0026rdot=1","price":"SGD聽99.95","list_price":"SGD聽142.79"},"TocLine":[{"Title":"The Tangent Structure ","Pid":"PA55","PgNum":"55","Order":69},{"Title":"Immersion and Submersion ","Pid":"PA127","PgNum":"127","Order":141},{"Title":"Curves and Hypersurfaces in Euclidean Space ","Pid":"PA143","PgNum":"143","Order":157},{"Title":"Lie Groups ","Pid":"PA189","PgNum":"189","Order":203},{"Title":"Fiber Bundles ","Pid":"PA257","PgNum":"257","Order":271},{"Title":"Tensors ","Pid":"PA307","PgNum":"307","Order":321},{"Title":"Differential Forms ","Pid":"PA345","PgNum":"345","Order":359},{"Title":"Integration and Stokes Theorem ","Pid":"PA391","PgNum":"391","Order":405},{"Title":"De Rham Cohomology ","Pid":"PA441","PgNum":"441","Order":455},{"Title":"Distributions and Frobenius Theorem ","Pid":"PA467","PgNum":"467","Order":481},{"Title":"Connections and Covariant Derivatives ","Pid":"PA501","PgNum":"501","Order":515},{"Title":"Riemannian and SemiRiemannian Geometry ","Pid":"PA547","PgNum":"547","Order":561},{"Title":"Appendix A The Language of Category Theory ","Pid":"PA637","PgNum":"637","Order":651},{"Title":"Appendix B Topology ","Pid":"PA643","PgNum":"643","Order":657},{"Title":"Modules and Multilinearity ","Pid":"PA649","PgNum":"649","Order":663},{"Title":"Bibliography ","Pid":"PA663","PgNum":"663","Order":677}]}},"table_of_contents_page_id":"PR5","max_resolution_image_width":1280,"max_resolution_image_height":1827,"num_toc_pages":5,"quality_info":"We have no quality information about this book.","volume_id":"QqHdHy9WsEoC","permission_info":"Pages displayed by permission of \u003ca class=link_aux href=\"https://books.google.com.sg/url?id=QqHdHy9WsEoC\u0026pg=PA7\u0026q=http://www.ams.org/bookstore\u0026clientid=ca-print-ams\u0026linkid=1\u0026usg=AOvVaw1q84riBerQzeD7iisJ3leq\u0026source=gbs_pub_info_r\"\u003eAmerican Mathematical Soc.\u003c/a\u003e","is_ebook":true,"volumeresult":{"has_flowing_text":false,"has_scanned_text":true,"can_download_pdf":false,"can_download_epub":false,"is_pdf_drm_enabled":false,"is_epub_drm_enabled":false},"publisher":"American Mathematical Soc.","publication_date":"2009","subject":"Mathematics","num_pages":671,"sample_url":"https://play.google.com/books/reader?id=QqHdHy9WsEoC\u0026source=gbs_vpt_hover","synposis":"\"Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry.\"--Publisher's website.","my_library_url":"https://www.google.com/accounts/Login?service=print\u0026continue=https://books.google.com.sg/books%3Fop%3Dlibrary\u0026hl=en","is_magazine":false,"is_public_domain":false,"last_page":{"pid":"PA675","order":689,"title":"675"}},{"enableUserFeedbackUI":true,"pseudocontinuous":true,"is_cobrand":false,"sign_in_url":"https://www.google.com/accounts/Login?service=print\u0026continue=https://books.google.com.sg/books%3Fid%3DQqHdHy9WsEoC%26pg%3DPA7%26redir_esc%3Dy%26hl%3Den\u0026hl=en","isEntityPageViewport":false,"showViewportOnboarding":false,"showViewportPlainTextOnboarding":false},{"page":[{"pid":"PA7","src":"https://books.google.com.sg/books/content?id=QqHdHy9WsEoC\u0026pg=PA7\u0026img=1\u0026zoom=3\u0026hl=en\u0026sig=ACfU3U1pgRQoGmtqFx8Bf_7DqIGm7a3lrw","flags":0,"order":21,"uf":"https://books.google.com.sg/books_feedback?id=QqHdHy9WsEoC\u0026spid=AFLRE70wq050Tcs8e0UfBUpk-j-wuHBfbVkJSjPMpUGcNSWGY3lMiL0JHvQ_zz2M1-A772d5mqe_\u0026ftype=0"},{"pid":"PA6","src":"https://books.google.com.sg/books/content?id=QqHdHy9WsEoC\u0026pg=PA6\u0026img=1\u0026zoom=3\u0026hl=en\u0026sig=ACfU3U2lRtHyJAhgAJQT4U6pVY0Y-zQuKw"},{"pid":"PA8","src":"https://books.google.com.sg/books/content?id=QqHdHy9WsEoC\u0026pg=PA8\u0026img=1\u0026zoom=3\u0026hl=en\u0026sig=ACfU3U38jrHZJg9SMuO9gnOeafdf-ImGzA"},{"pid":"PA9","src":"https://books.google.com.sg/books/content?id=QqHdHy9WsEoC\u0026pg=PA9\u0026img=1\u0026zoom=3\u0026hl=en\u0026sig=ACfU3U3GuNJTiNHtQkiaddBq6VU3oG6lAw"},{"pid":"PA10","src":"https://books.google.com.sg/books/content?id=QqHdHy9WsEoC\u0026pg=PA10\u0026img=1\u0026zoom=3\u0026hl=en\u0026sig=ACfU3U0ANRyJ7eRtTFy0hkmOUBHGNjRJYw"}]},null,null,{});</script></div></div></div><script>(function() {var href = window.location.href;if (href.indexOf('?') !== -1) {var parameters = href.split('?')[1].split('&');for (var i = 0; i < parameters.length; i++) {var param = parameters[i].split('=');if (param[0] == 'focus') {var elem = document.getElementById(param[1]);if (elem) {elem.focus();}}}}})();</script>

Pages: 1 2 3 4 5 6 7 8 9 10