{"id":8948,"date":"2010-02-19T15:46:00","date_gmt":"2010-02-19T15:46:00","guid":{"rendered":"http:\/\/melotopia.net\/b\/?p=8948"},"modified":"2010-02-19T15:46:00","modified_gmt":"2010-02-19T15:46:00","slug":"%ed%85%90%ec%84%9c","status":"publish","type":"post","link":"http:\/\/melotopia.net\/b\/?p=8948","title":{"rendered":"\ud150\uc11c"},"content":{"rendered":"
\n Chern \uc120\uc0dd\ub2d8\uc758 \ubbf8\ubd84\uae30\ud558\ud559 \uac15\uc758 \ucc45\uc744 \ubcf4\uace0 \uc788\ub2e4.
\n
\n Lectures on Differential Geometry (Series on University Mathematics Vol. 1)
\n
\n S. S. Chern, W. H. Chen, K. S. Lam.<\/p>\n

\ud1a0\ub098\uc624\uac8c \uc5b4\ub835\uc9c0\ub9cc…
\n
\n \uc544\ub2c8 \uadfc\ub370 “\ub300\ud559 \uc218\ud559 \uc2dc\ub9ac\uc988”\uc778\ub370 \ub300\ud559\uc6d0\uae4c\uc9c0 \ub098\uc628 \ub0b4\uac00 \uc774\ud574\ub97c \ubabb\ud558\uaca0\ub294\uac78\uae4c -_-;
\n
\n \ud655\uc2e4\ud788 \uae30\ud558\ud559\uc740 \ub098\uc5d0\uac8c \ub118\uc0ac\ubcbd\uc778\uac00. \ud559\ubd80\ub54c \ubc30\uc6b4 Elementary Differential Geometry\uac00 \uc9c4\uc9dc “Elementary” \uc218\uc900\uc774\ub77c\ub294 \uac83\uc744 \uc5ec\uc2e4\ud788 \ub290\ub07c\uace0 \uc788\ub2e4. \uc544\ubb34\ud2bc.<\/p>\n

\uac04\ub2e8\ud788 \uba87\uac00\uc9c0 \uac1c\ub150\ub9cc \uc815\ub9ac\ud558\uace0 \uac00\uc57c\uaca0\ub2e4.
\n
\n Manifold : Manifold\ub294 \uc5b4\ub5a4 \ud2b9\uc815\ud55c \uc885\ub958\uc758 \uc9d1\ud569\uc774\ub2e4. (\uacf5\uac04 \uac19\uc740\uac70) \uc774 \uc9d1\ud569 \uc548\uc5d0 \uc788\ub294 \uc5b4\ub5a4 \uc6d0\uc18c\uc5d0 \ub300\ud574\uc11c, \uadf8 \uadfc\ubc29\uc5d0 \uc788\ub294 \uc801\ub2f9\ud55c \uc9d1\ud569\uc774 m\ucc28\uc6d0 \uc2e4\uc218 \ubca1\ud130 \uacf5\uac04\uc758 \uc801\ub2f9\ud55c \uc5f4\ub9b0 \ubd80\ubd84 \uc9d1\ud569\uc73c\ub85c homeomorphic\ud558\uba74 \uc774 \uc9d1\ud569\uc774 Manifold\uc774\ub2e4.
\n
\n \uc27d\uac8c \ub9d0\ud574\uc11c, \ubc94\uc704\ub97c \uc881\ud600\uc11c \ubcf4\uba74 \ud3c9\ubc94\ud55c \ubca1\ud130 \uacf5\uac04\ucc98\ub7fc \ubcf4\uc774\ub294 \uacf5\uac04\uc774\ub2e4. \uc6b0\ub9ac\ub9d0\ub85c\ub294 “\ub2e4\uc591\uccb4”\ub77c\uace0 \ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uad6c\uba74\uc740 \uc544\uc8fc \uc791\uc740 \ubc94\uc704\uc5d0\uc11c\ub294 \ud3c9\uba74\uacfc \ube44\uc2b7\ud558\ub2c8\uae4c \ub2e4\uc591\uccb4\uac00 \ub41c\ub2e4.<\/p>\n

Tangent space : \uc5b4\ub5a4 manifold \uc5d0\uc11c, \ud2b9\uc815\ud55c \uc810\uc744 \uc6d0\uc810\uc73c\ub85c \ud558\ub294 \ubca1\ud130\ub4e4\uc758 \ubca1\ud130 \uacf5\uac04. \uc218\ud559\uc801\uc73c\ub85c \uc5c4\ubc00\ud558\uac8c \uc815\uc758\ud558\ub824\uba74 \ub354 \ubcf5\uc7a1\ud55c \uc218\uc2dd\uc73c\ub85c \ub354 \uc5c4\ubc00\ud558\uac8c \uc774\ub860\uc744 \uc804\uac1c\ud574\uc57c \ud558\uc9c0\ub9cc, \ub098\ub3c4 \uc774\ud574\uac00 \uc548\ub418\ubbc0\ub85c \uc5ec\uae30\uc11c \uc904\uc778\ub2e4. \uadf8\ub098\uc800\ub098, \uc774 \uacf5\uac04\uc5d0\uc11c \ubca1\ud130\uc758 \uae38\uc774\ub294 \ubcc4\ub85c \uc2e0\uacbd\uc744 \uc548\uc4f0\ub294 \uac83 \uac19\ub2e4.<\/p>\n

Poisson bracket product : X, Y\uac00 \uc5b4\ub5a4 tangent space\uc5d0 \uc18d\ud55c \ub450 \ubca1\ud130\ub77c\uace0 \ud560 \ub54c, [X, Y] = XY – YX \uc774\ub2e4. \uc5ec\uae30\uc11c -\ub294 \uadf8\ub0e5 \ubca1\ud130\ub4e4\ub07c\ub9ac \ube7c\ub294 \uac83\uc774\uace0 XY\ub294, \uc2e4\uc81c\ub85c tangent space\ub97c \uc815\uc758\ud560 \ub54c “\ud2b9\uc815\ud55c \uc810\uc744 \uc6d0\uc810\uc73c\ub85c \ud558\ub294 \ubca1\ud130”\ub97c \uc0ac\uc6a9\ud574\uc11c \uc815\uc758\ud558\ub294\ub370, \uc774\ub54c X\ub098 Y\ub4e4\uc744 \uc5f0\uc0b0\uc790\ub85c \uc815\uc758\ud55c\ub2e4. XY\ub294 \ud574\ub2f9 \ud2b9\uc815\ud55c \uc810\uc5d0 \ub300\ud55c \uc5f0\uc0b0\uc790\ub97c Y\ub97c \uba3c\uc800 \uc791\uc6a9\ud558\uace0 X\ub97c \ub098\uc911\uc5d0 \uc791\uc6a9\ud55c\ub2e4\ub294 \ub73b\uc774\ub2e4. \uc774\ucbe4 \uc124\uba85\ud588\uc73c\uba74 \ub2e4\ub4e4 \ubabb\uc54c\uc544\ub4e4\uc5c8\uc744 \uac83\uc774\ub2e4. \ud558\uc9c0\ub9cc \ub098\ub3c4 \ubaa8\ub974\ub294\uac78 \uc774\ubcf4\ub2e4 \ub354 \uc27d\uac8c \uc124\uba85\ud558\ub294 \uac83\uc740 \ubd88\uac00\ub2a5\ud558\ub2e4.<\/p>\n

Frobenius Theorem : \uadf8\ub4e4\uc740 Frobenius \uc870\uac74\uc744 \ub9cc\uc871\ud558\uac8c \ub41c\ub2e4…
\n
\n \uc774\ud574\ud558\uace0 \uc2f6\uc740 \uc815\ub9ac \uc911\uc758 \ud558\ub098. \uc544\ub2c8, \uadf8\ubcf4\ub2e4\ub294, \uc774\ud574\ub294 \ud588\ub294\ub370 \uc774\ud574\ud588\ub358 \ub0b4\uc6a9\uc744 \uc78a\uc5b4\uc11c Chapter 1\uc744 \ubabb \ub118\uc5b4\uac00\uac8c \ud558\ub294 \uc6d0\uc778\uc774 \ub418\ub294 \uc815\ub9ac. \uc0ac\uc2e4\uc740 \uae30\uc5b5\ud558\uace0 \uc2f6\uc740 \uc815\ub9ac\uc911\uc758 \ud558\ub098\ub2e4. \ub098\uc911\uc5d0 \ucc45 \uc77d\ub2e4\uac00 \uc368\uba39\ub294 \ubd80\ubd84\uc774 \ub098\uc624\uba74 \uadf8\ub54c \ub2e4\uc2dc \ubcf5\uc2b5\ud558\uae30\ub85c \ud558\uace0 \uc77c\ub2e8 \ub118\uc5b4\uac04\ub2e4.<\/p>\n

\ubca1\ud130 \uacf5\uac04 : \uc774\uac74 \ub2e4\ub4e4 \uc54c\ub2e4\uc2dc\ud53c, \ub367\uc148 \uc798\ub418\uace0 \uae38\uc774 \uc798 \ubc14\ub00c\ub294 \uac83\ub4e4\uc758 \uacf5\uac04\uc774\ub2e4.
\n
\n \ubca1\ud130 \uacf5\uac04\uc758 Dual : \ubca1\ud130 \uacf5\uac04\uc5d0\uc11c \ubc8c\uc5b4\uc9c0\ub294 \ubca1\ud130\ub9e8\uacfc \uce68\ub7b5\uc790\ub4e4 \uc0ac\uc774\uc758 1\ub300 1 \uc2f8\uc6c0\uc774 \uc544\ub2c8\ub2e4. \uc815\ud655\ud788\ub294, \ubca1\ud130\uacf5\uac04\uc5d0\uc11c \uc2a4\uce7c\ub77c \uac12\uc744 \uac16\ub294 \ud568\uc218\ub4e4\uc758 \uc9d1\ud569\uc774\ub2e4. \ub2e8, \uc774\ub54c \uc774 \ud568\uc218\ub4e4 \ub610\ud55c \ubca1\ud130 \uacf5\uac04\uc744 \uc774\ub8ec\ub2e4. \uadf8\ub54c \ud568\uc218\ub4e4\uc774 \uc774\ub8e8\ub294 \ubca1\ud130 \uacf5\uac04\uc744 dual \uacf5\uac04\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. dual \ub07c\ub9ac\ub294 \uc11c\ub85c Dual\uc774\ub2e4. \uc6b0\ub9ac\ub9d0\ub85c\ub294 “\uc30d\ub300 \uacf5\uac04”\uc774\ub77c\uace0 \ud558\ub294\ub370, \uc5ed\uc2dc \uc775\uc219\ud574 \uc9c0\uc9c0 \uc54a\ub294 \ud55c\uae00 \uc218\ud559\uc6a9\uc5b4\ub2e4.<\/p>\n

\ud150\uc11c \uacf1(Tensor product) : \uc6d0\ub798 Cartesian product\ub77c\ub294 \uac83\uc740, \uc801\ub2f9\ud788 \ubaa8\uc544\uc628 \uc5ec\ub7ec\uac1c\uc758 \uc9d1\ud569\uc5d0\uc11c \uac01 \uc9d1\ud569\ub9c8\ub2e4 \uc6d0\uc18c\ub97c \ud558\ub098\uc529 \uaebc\ub0b4\uc11c \uad04\ud638 \uc548\uc5d0 \ub123\uace0, “\uc774\uc81c \ub108\ub124\ub294 \ud55c\ubab8\uc774\uc57c”\ub77c\uace0 \uc120\uc5b8\ud558\uace0 \uadf8\ub7f0\uac83\ub4e4\ub85c \uc0c8\ub85c\uc6b4 \uc9d1\ud569\uc744 \uad6c\uc131\ud558\ub294 \uac83\uc774\ub2e4. (\uc218\ud559\uc5d0\uc11c\ub294 \uc5ec\ub7ec\uac1c\ub97c \ubb36\uc5b4\uc11c \ud558\ub098\ub85c \ub9cc\ub4dc\ub294 \uac78 \ub300\ucda9 product\ub77c\uace0 \ubd80\ub978\ub2e4.) \uadfc\ub370 Tensor \uacf1\uc774\ub77c\ub294 \uac83\uc740 \uadf8\ub807\uac8c \ub9cc\ub4e4\uc5b4 \ub193\uc740 \uc9d1\ud569\uc5d0\uc11c, \ub2e4\ub978 \uc0c8\ub85c\uc6b4 \ubca1\ud130 \uacf5\uac04\uc73c\ub85c \uac00\ub294 \ud568\uc218\uc640 \ud568\uaed8 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\n

\ud150\uc11c : \uc5b4\ub5a4 \ubca1\ud130 \uacf5\uac04 V\uc5d0 \ub300\ud574\uc11c, V\ub97c \uc5ec\ub7ec\ubc88 \ubb36\uace0 V\uc758 dual \uacf5\uac04\uc744 \uc5ec\ub7ec\ubc88 \ubb36\uc5b4\uc11c \ud55c\ubab8\uc73c\ub85c \ub9cc\ub4e0 \uac83\uc744 \ud150\uc11c\ub77c\uace0 \ud55c\ub2e4. \uc989, \uc544\ubb34\ud2bc\uac04\uc5d0 \ud558\ub098\uc758 \ubca1\ud130 \uacf5\uac04\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ud150\uc11c \uacf1\uc744 \ud150\uc11c\ub77c\uace0 \ubd80\ub978\ub2e4. \ud589\ub82c\uc758 \ud655\uc7a5\ub41c \ud615\ud0dc\ub77c\uace0 \ubcf4\uba74 \ub41c\ub2e4. \ud558\ub098\uc758 \uacf5\uac04\uc5d0\uc11c \uc6d0\uc18c\ub4e4\uc744 \ubf51\uc544 \uc654\uae30 \ub54c\ubb38\uc5d0, \uc778\ub371\uc2a4\ub07c\ub9ac \ubc14\uafb8\ub354\ub77c\ub3c4 \uc5ec\uc804\ud788 \ud150\uc11c\ub85c\uc11c \uc720\ud6a8\ud558\ub2e4. (\uc77c\ubc18\uc801\uc778 \ud150\uc11c \uacf1\uc77c \ub54c\ub294 \uc778\ub371\uc2a4\uc758 \uc21c\uc11c\ub97c \ubc14\uafb8\uba74 \uc624\ub958\uac00 \ubc1c\uc0dd\ud55c\ub2e4.)<\/p>\n

\ud150\uc11c \ub300\uc218 : \ub09c 4\ub144\uac04 \uc218\ud559\uc744 \ubc30\uc6cc\uc654\uc9c0\ub9cc \uc544\uc9c1\ub3c4 Algebra\ub77c\ub294 \ub9d0\uc758 \uc815\ud655\ud55c \ub73b\uc744 \ubaa8\ub974\uaca0\ub2e4. \ud150\uc11c \ub300\uc218\ub780 \ubca1\ud130 \uacf5\uac04 V\ub97c 0\ubc88, 1\ubc88, 2\ubc88, … \uc368\uc11c \ub9cc\ub4e0 \ubaa8\ub4e0 \ud150\uc11c\ub97c \uc804\ubd80 \ud569\uccd0\uc11c(direct sum) \ub9cc\ub4e0 \uadf8\ub7f0 \uacf5\uac04\uc774\ub2e4. \uc774 \uacf5\uac04\uc5d0 \uc788\ub294 \uc6d0\uc18c\ub4e4\uc740 \uc544\ubb34\uac70\ub098 \ubf51\uc544\ub2e4\uac00 \ud569\uccd0(direct sum)\ub3c4 \ub2e4\uc2dc \uc774 \uc548\uc5d0 \ub4e4\uc5b4\uc624\uae30 \ub54c\ubb38\uc5d0 Algebra\uac00 \ub41c\ub2e4\uace0 \ud55c\ub2e4.<\/p>\n

\uc678\ubd80 \ub300\uc218 : Exterior algebra\ub294, \ubc18\ub300\uce6d\uc131 contravariant \ud150\uc11c\uc774\ub2e4.<\/p>\n

…<\/p>\n

\uc5ec\uae30\uae4c\uc9c0\uac00 \uad50\uc7ac 2\uc7a5\uae4c\uc9c0\uc758 \ub0b4\uc6a9 \uc911 \uba38\ub9bf\uc18d\uc5d0 \ud3d0\ud5c8\ub85c\ub77c\ub3c4 \ub0a8\uc544\uc788\ub294 \ub0b4\uc6a9\uc744 \uc815\ub9ac\ud55c \uac83\uc774\ub2e4. 3\uc7a5\uc5d0\uc120 \ud150\uc11c \ubb36\uc74c\uacfc \ubca1\ud130 \ubb36\uc74c\uc774 \ub098\uc628\ub2e4.<\/p>\n

\uc880 \ub354 \uc77d\uc5b4\ubcf4\uace0 \ub2e4\uc74c \uae00\uc744 \uc368\ubcf4\ub3c4\ub85d \ud558\uaca0\ub2e4. \ub09c \uc5ed\uc2dc \ud574\uc11d\ud559\uc774 \uc88b\uc740 \uac83 \uac19\ub2e4.<\/p>\n

\n
\n
\n\"\uc2e0\uace0\"
\n<\/a>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Chern \uc120\uc0dd\ub2d8\uc758 \ubbf8\ubd84\uae30\ud558\ud559 \uac15\uc758 \ucc45\uc744 \ubcf4\uace0 \uc788\ub2e4. Lectures on Differential Geometry (Series on University Mathematics Vol. 1) S. S. Chern, W. H. Chen, K. S. Lam. \ud1a0\ub098\uc624\uac8c \uc5b4\ub835\uc9c0\ub9cc… \uc544\ub2c8 \uadfc\ub370 “\ub300\ud559 \uc218\ud559 \uc2dc\ub9ac\uc988”\uc778\ub370 \ub300\ud559\uc6d0\uae4c\uc9c0 \ub098\uc628 \ub0b4\uac00 \uc774\ud574\ub97c \ubabb\ud558\uaca0\ub294\uac78\uae4c -_-; \ud655\uc2e4\ud788 \uae30\ud558\ud559\uc740 \ub098\uc5d0\uac8c \ub118\uc0ac\ubcbd\uc778\uac00. \ud559\ubd80\ub54c \ubc30\uc6b4 Elementary Differential Geometry\uac00 \uc9c4\uc9dc “Elementary” \uc218\uc900\uc774\ub77c\ub294 \uac83\uc744 \uc5ec\uc2e4\ud788 \ub290\ub07c\uace0 \uc788\ub2e4. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-8948","post","type-post","status-publish","format-standard","hentry","category-academic"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8o6gA-2kk","jetpack-related-posts":[],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/8948","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8948"}],"version-history":[{"count":0,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/8948\/revisions"}],"wp:attachment":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8948"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8948"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8948"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}