{"id":3689,"date":"2013-08-06T17:22:19","date_gmt":"2013-08-06T09:22:19","guid":{"rendered":"http:\/\/lttt.blog.ustc.edu.cn\/?p=3689"},"modified":"2013-08-06T17:22:19","modified_gmt":"2013-08-06T09:22:19","slug":"%e6%ae%86%e5%a4%8d%e6%b5%81%e5%bd%a2%e4%b8%8a%e5%8f%af%e4%bb%a5%e5%ae%9a%e4%b9%89%e5%85%a8%e7%ba%af%e5%90%91%e9%87%8f%e4%b8%9b%e4%b9%88","status":"publish","type":"post","link":"https:\/\/lttt.vanabel.cn\/?p=3689","title":{"rendered":"\u6b86\u590d\u6d41\u5f62\u4e0a\u53ef\u4ee5\u5b9a\u4e49\u5168\u7eaf\u5411\u91cf\u4e1b\u4e48"},"content":{"rendered":"
Problem . <\/strong>\u6211\u4eec\u77e5\u9053, \u5728\u590d\u6d41\u5f62$M$\u4e0a, \u53ef\u4ee5\u8bc1\u660e$T^{1,0}M$\u662f$M$\u4e0a\u7684\u4e00\u4e2a\u5168\u7eaf\u5411\u91cf\u4e1b.<\/p>\n

\u90a3\u4e48\u5bf9\u4e00\u822c\u7684\u6b86\u590d\u6d41\u5f62, \u6211\u4eec\u662f\u5426\u8fd8\u6709\u8fd9\u4e2a\u7ed3\u8bba\u6210\u7acb\u5462?<\/p>\n<\/div>\n

\u9996\u5148, \u4e5f\u8bb8\u8981\u770b\u770b\u6b86\u590d\u6d41\u5f62\u4e0a\u80fd\u4e0d\u80fd\u5b9a\u4e49\u5168\u7eaf\u6620\u5c04. \u8fd9\u662f\u53ef\u4ee5\u7684, \u7528\u5916\u5fae\u5206\u7b97\u5b50\u9650\u5236\u5230$T^{1,0}M$\u90e8\u5206\u5373\u53ef, \u770b\u8d77\u6765\u6211\u4eec\u4f3c\u4e4e\u53ef\u4ee5\u5b9a\u4e49\u6b86\u590d\u6d41\u5f62\u4e0a\u7684\u5168\u7eaf\u5411\u91cf\u4e1b. \u4f46\u662f\u67e5\u9605\u6587\u732e\u5374\u57fa\u672c\u662f\u5426\u5b9a\u7684\u7b54\u6848.<\/p>\n

\u5728\u65871<\/a>\u4e2d,<\/p>\n

Note, that $X$ is in general only a differentiable manifold and thus there is
\nno concept of holomorphy<\/em>: The holomorphic tangent bundle $T^{1,0} X$ can not be
\na holomorphic vector bundle on a differentiable manifold. If $X$ is complex,
\nhowever, one has that $T^{1,0} X = TX$ is indeed the holomorphic tangent bundle
\nof $X$.<\/p><\/blockquote>\n

\u5728wiki\u4e2d\u6709\u4e2aTalk2<\/a>, \u63d0\u5230locally holomorphic vector bundle<\/em>\u53ef\u4ee5\u5b9a\u4e49.<\/p>\n

\u4e5f\u8bb8\u6587\u7ae0Nonorientable manifolds, complex structures, and holomorphic vector bundles<\/em>3<\/a>\u503c\u5f97\u4e00\u770b.<\/p>\n

\n
\n
    \n
  1. http:\/\/www.mathematik.hu-berlin.de\/~berg\/Almost_Complex_Manifolds_Seminar_2011_03_07.pdf<\/a> \u21a9<\/a><\/li>\n
  2. http:\/\/en.wikipedia.org\/wiki\/Talk:Almost_complex_manifold#Holomorphic.3F<\/a> \u21a9<\/a><\/li>\n
  3. Biswas, Indranil, and Avijit Mukherjee. “Nonorientable manifolds, complex structures, and holomorphic vector bundles.” Acta Applicandae Mathematica<\/em> 69.1 (2001): 25-42. \u21a9<\/a><\/li>\n<\/ol>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

    Problem . \u6211\u4eec\u77e5\u9053, \u5728\u590d\u6d41\u5f62$M$\u4e0a, \u53ef\u4ee5\u8bc1\u660e$T^{1,0}M$ …<\/p>\n

    \u6b86\u590d\u6d41\u5f62\u4e0a\u53ef\u4ee5\u5b9a\u4e49\u5168\u7eaf\u5411\u91cf\u4e1b\u4e48<\/span> \u9605\u8bfb\u66f4\u591a »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[213,736],"class_list":["post-3689","post","type-post","status-publish","format-standard","hentry","category-mathnotes","tag-213","tag-736"],"_links":{"self":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/3689","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3689"}],"version-history":[{"count":0,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/3689\/revisions"}],"wp:attachment":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}