[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/19852#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/19852","headline":"\u6e2c\u5730\u5ddd – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"\u6e2c\u5730\u5ddd – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u6570\u5b66\u3068\u7269\u7406\u5b66\u3067\u306f\u3001 \u6e2c\u5730\u5ddd \u6700\u77ed\u306e\u63a5\u7d9a\u30e9\u30a4\u30f3\uff08\u30b8\u30aa\u30c7\uff09\u306b\u6cbf\u3063\u305f\u52d5\u304d\u3002\u30b8\u30aa\u30c7\u306f\u51fa\u767a\u70b9\u3060\u3051\u3067\u306a\u304f\u3001\u958b\u59cb\u65b9\u5411\u306b\u3082\u4f9d\u5b58\u3059\u308b\u305f\u3081\u3001\u6e2c\u5730\u5ddd\u306f\u63a5\u7dda\u30d0\u30f3\u30c9\u30eb\u3067\u306e\u307f\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002 after-content-x4 \u305d\u3046\u3067\u3059 m {displaystyle m} \u63a5\u7dda\u30d0\u30f3\u30c9\u30eb\u3092\u5099\u3048\u305f\u5b8c\u5168\u306aRiemann\u306e\u591a\u69d8\u6027 t m {displaystyleTm} \u3002 Hopf-Rinow\u306e\u5224\u6c7a\u306b\u3088\u308b\u3068\u3001\u3059\u3079\u3066\u306e\u63a5\u7dda\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308a\u307e\u3059 after-content-x4 \u306e \u2208 t xm","datePublished":"2021-09-21","dateModified":"2021-09-21","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f82cade9898ced02fdd08712e5f0c0151758a0dd","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f82cade9898ced02fdd08712e5f0c0151758a0dd","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/19852","wordCount":5005,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u6570\u5b66\u3068\u7269\u7406\u5b66\u3067\u306f\u3001 \u6e2c\u5730\u5ddd \u6700\u77ed\u306e\u63a5\u7d9a\u30e9\u30a4\u30f3\uff08\u30b8\u30aa\u30c7\uff09\u306b\u6cbf\u3063\u305f\u52d5\u304d\u3002\u30b8\u30aa\u30c7\u306f\u51fa\u767a\u70b9\u3060\u3051\u3067\u306a\u304f\u3001\u958b\u59cb\u65b9\u5411\u306b\u3082\u4f9d\u5b58\u3059\u308b\u305f\u3081\u3001\u6e2c\u5730\u5ddd\u306f\u63a5\u7dda\u30d0\u30f3\u30c9\u30eb\u3067\u306e\u307f\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u305d\u3046\u3067\u3059 m {displaystyle m} \u63a5\u7dda\u30d0\u30f3\u30c9\u30eb\u3092\u5099\u3048\u305f\u5b8c\u5168\u306aRiemann\u306e\u591a\u69d8\u6027 t m {displaystyleTm} \u3002 Hopf-Rinow\u306e\u5224\u6c7a\u306b\u3088\u308b\u3068\u3001\u3059\u3079\u3066\u306e\u63a5\u7dda\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308a\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u306e \u2208 t xm \u3001 \u30d0\u30c4 \u2208 m {displaystyle vin t_ {x} m\u3001m}\u3092\u304a\u9858\u3044\u3057\u307e\u3059 \u660e\u78ba\u306a\u30b8\u30aa\u30c7 \u03b3v\uff1a \uff08  –  \u221e \u3001 \u221e \uff09\uff09 \u2192 m {displaystyle\u30ac\u30f3\u30de_ {v}\u30b3\u30ed\u30f3\uff08-infty\u3001infty\uff09\u304b\u3089m} \u3068        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u03b3v\uff08 0 \uff09\uff09 = \u30d0\u30c4 \u3001 \u03b3\u02d9v\uff08 0 \uff09\uff09 = \u306e {displaystyle gamma _ {v}\uff080\uff09= x\u3001{dot {gamma}} _ {v}\uff080\uff09= v} \u3002 \u3053\u308c\u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059 \u03d5 \uff1a t m \u00d7 \uff08  –  \u221e \u3001 \u221e \uff09\uff09 \u2192 t m {displaystyle phi colon tmtimes\uff08-infty\u3001infty\uff09\u304b\u3089tm} \u7d42\u3048\u305f \u03d5 \uff08 \u306e \u3001 t \uff09\uff09 \uff1a= \u03b3\u02d9v\uff08 t \uff09\uff09 {displaystyle phi\uff08v\u3001t\uff09\uff1a= {dot {gamma}} _ {v}\uff08t\uff09} \u3002 \u3053\u308c\u306f\u5ddd\u3092\u5b9a\u7fa9\u3057\u307e\u3059 t m {displaystyleTm} \u3001d\u3002 H.\u9069\u7528\u3055\u308c\u307e\u3059 \u03d5 \uff08 \u306e \u3001 s + t \uff09\uff09 = \u03d5 \uff08 \u03d5 \uff08 \u306e \u3001 t \uff09\uff09 \u3001 s \uff09\uff09 {displaystyle phi\uff08v\u3001s+t\uff09= phi\uff08phi\uff08v\u3001t\uff09\u3001s\uff09} \u3068 \u03d5 \uff08 \u306e \u3001 0 \uff09\uff09 = \u306e {displaystyle phi\uff08v\u30010\uff09= v} \u3002 \u591a\u304f\u306e\u5834\u5408\u3001\u30e6\u30cb\u30c3\u30c8\u30ed\u30c3\u30c9\u30d0\u30f3\u30c9\u30eb\u3078\u306e\u6e2c\u5730\u5ddd\u306e\u5236\u9650 t 1m {displaystylet^{1} m} \u6e2c\u5730\u5ddd\u3068\u547c\u3070\u308c\u307e\u3059\u3002 \u6e2c\u5730\u5ddd\u306f\u3001\u30cf\u30df\u30eb\u30c8\u30f3\u306e\u5730\u5143\u306e\u5ea7\u6a19\u306e\u6d41\u308c\u3067\u3059 h \uff08 \u30d0\u30c4 \u3001 p \uff09\uff09 \uff1a= 12\u2211i,jgij\uff08 \u30d0\u30c4 \uff09\uff09 pipj{displaystyle h\uff08x\u3001p\uff09\uff1a= {frac {1} {2}} sum _ {i\u3001j} g^{ij}\uff08x\uff09p_ {i} p_ {j}} \u30cf\u30df\u30eb\u30c8\u30f3\u6a5f\u80fd\u304c\u4e0e\u3048\u3089\u308c\u305f h \uff1a T\u2217m \u2192 R{displaystyle hcolon t^{*} mto mathbb {r}} \u3002 \u3053\u3061\u3089\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044 g ij\uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle g^{ij}\uff08x\uff09} Riemann Metrik\u306e\u30a8\u30f3\u30c8\u30ea g ij\uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle g_ {ij}\uff08x\uff09} \u30a4\u30f3\u30d0\u30fc\u30bb\u30f3\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3002 \u525b\u4f53\u306e\u52d5\u304d\u306e\u30aa\u30a4\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306f\u3001\u5618\u30b0\u30eb\u30fc\u30d7\u306e\u6e2c\u5730\u7684\u306a\u6d41\u308c\u3068\u3057\u3066\u89e3\u91c8\u3067\u304d\u307e\u3059 \u79c1 s o m \uff08 R3\uff09\uff09 {displaysyllllle mathrm {isom}\uff08mathbb {r} ^ {3} \u3002 \u975e\u5727\u7e2e\u6027\u5ddd\u306e\u6d41\u4f53\u30c0\u30a4\u30ca\u30df\u30af\u30b9\u4e0a\u306e\u30aa\u30a4\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306f\u3001\u7121\u9650\u6b21\u5143\u306e\u5618\u30b0\u30eb\u30fc\u30d7\u306e\u6e2c\u5730\u7684\u306a\u6d41\u308c\u3068\u3057\u3066\u89e3\u91c8\u3067\u304d\u307e\u3059 s d \u79c1 f f \uff08 R3\uff09\uff09 {displaystyle mathrm {sdiff}\uff08mathbb {r} ^{3}\uff09} \u52a9\u6210\u91d1\u306e\u6442\u53d6\u30a4\u30e9\u30b9\u30c8\u306e\u3002 \u3069\u3061\u3089\u306e\u89e3\u91c8\u3082\u30a6\u30e9\u30b8\u30df\u30fc\u30eb\u30a2\u30fc\u30ce\u30eb\u30c9\u306b\u623b\u308a\u307e\u3059\u3002 [\u521d\u3081] Table of Contents\u975e\u30dd\u30b9\u30c8\u30d1\u30f3\u7c89\u306e\u30de\u30cb\u30db\u30fc\u30eb\u30c9\u4e0a\u306e\u6e2c\u5730\u5ddd [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u7406\u8ad6\u3092\u6e2c\u5b9a\u3057\u307e\u3059 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5b89\u5b9a\u3057\u305f\u4e0d\u5b89\u5b9a\u306a\u30de\u30cb\u30db\u30fc\u30eb\u30c9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u7121\u9650\u306e\u7403\u4f53\u306e\u30c0\u30a4\u30ca\u30df\u30af\u30b9\u3068\u306e\u95a2\u4fc2 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4f8b\uff1a\u53cc\u66f2\u7dda\u30ec\u30d9\u30eb [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u975e\u30dd\u30b9\u30c8\u30d1\u30f3\u7c89\u306e\u30de\u30cb\u30db\u30fc\u30eb\u30c9\u4e0a\u306e\u6e2c\u5730\u5ddd [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4ee5\u4e0b\u3067\u3042\u308a m {displaystyle m} \u975e\u4f4d\u7f6e\u7684\u306a\u66f2\u7387\u306e\u30ea\u30fc\u30de\u30f3\u306e\u591a\u69d8\u6027\u3002 \u7406\u8ad6\u3092\u6e2c\u5b9a\u3057\u307e\u3059 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6e2c\u5730\u5ddd\u306f\u30ea\u30a6\u30d3\u30eb\u306e\u30b5\u30a4\u30ba\u3092\u53d7\u3051\u53d6\u308a\u307e\u3059\u3002\u3082\u3057\u3082 m {displaystyle m} \u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3001\u6e2c\u5730\u5ddd\u306f\u30a8\u30eb\u30b4\u30b8\u30c3\u30af\u3067\u3059\u3002 [2] [3] \u3053\u306e\u5834\u5408\u3001\u5f7c\u306f\u307e\u305f\u3001\u6307\u6570\u95a2\u6570\u7684\u306b\u6df7\u5408\u3057\u3066\u304a\u308a\u3001\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u304c\u6b63\u3001\u5bc6\u306a\u8ecc\u9053\u304c\u3042\u308a\u3001\u5468\u671f\u8ecc\u9053\u306e\u91cf\u306f\u304d\u3064\u304f\u3001\u7121\u9650\u306e\uff08\u7dda\u5f62\u975e\u4f9d\u5b58\u6027\u306e\uff09\u4e0d\u5909\u5bf8\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002 \u5b89\u5b9a\u3057\u305f\u4e0d\u5b89\u5b9a\u306a\u30de\u30cb\u30db\u30fc\u30eb\u30c9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3082\u3057\u3082 m {displaystyle m} \u6e2c\u5730\u5ddd\u306f\u30a2\u30ce\u30bd\u30d5\u5ddd\u3067\u3059\uff08\u305d\u3057\u3066\u3001\u3088\u308a\u5f31\u3044\u6761\u4ef6\u4e0b\u3067\u3082\uff09\u3002 \u7121\u9650\u306e\u7403\u4f53\u306e\u30c0\u30a4\u30ca\u30df\u30af\u30b9\u3068\u306e\u95a2\u4fc2 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3082\u3057\u3082 m {displaystyle m} \u975e\u967d\u6027\u306e\u30d1\u30f3\u7c89\u304c\u3042\u308a\u3001\u6e2c\u5730\u5ddd\u306f\u30cf\u30a4\u30ad\u30f3\u30b0\u3067\u306f\u306a\u304f\u3001\u6b21\u306b pi 1m {displaystyle pi _ {1} m} \u7121\u9650\u306e\u7403\u4f53 \u2202 \u221eM~{displaystyle partial _ {infty} {widetilde {m}}} \u6e2c\u5730\u5ddd\u304c\u5358\u4f4d\u89d2\u5ea6\u306e\u30d0\u30f3\u30c9\u30eb\u306b\u5bc6\u5ea6\u304c\u3042\u308b\u5834\u5408\u3001\u6b63\u78ba\u306b\u5bc6\u5ea6\u3002 \u4f8b\uff1a\u53cc\u66f2\u7dda\u30ec\u30d9\u30eb [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ]  \u53cc\u66f2\u7dda\u30ec\u30d9\u30eb\u306e\u30dd\u30a2\u30f3\u30ab\u30ec\u30e2\u30c7\u30eb\u3001\u540c\u3058\u30dd\u30a4\u30f3\u30c8\uff08\u8d64\uff09\u3067\u7d42\u4e86\u3059\u308b\u3055\u307e\u3056\u307e\u306a\u30b8\u30aa\u30fc\u30c7\u3068\u95a2\u9023\u3059\u308b\u30db\u30ed\u30b5\u30a4\u30af\u30eb\uff08\u9752\uff09\u3002 \u305d\u3046\u3067\u3059 h 2{displaystyle h^{2}} \u53cc\u66f2\u7dda\u30ec\u30d9\u30eb\u3068 t 1h 2{displaystyle t^{1} h^{2}} \u30e6\u30cb\u30c3\u30c8\u30a8\u30c3\u30b8\u30d0\u30f3\u30c9\u30eb\u3002\u65b9\u5411\u306e\u30b0\u30eb\u30fc\u30d7\u306e\u52b9\u679c – \u62e1\u5f35\u578b\u30a4\u30bd\u30e1\u30c8\u30ea Isom+\uff08 H2\uff09\uff09 \u2243 PSL\uff08 2 \u3001 R\uff09\uff09 {displaystyle mathrm {isom} ^{+}\uff08h ^{2}\uff09simeq {psl}\uff082\u3001mathbb {r}\uff09} \u306e\u4e0a t 1h 2{displaystyle t^{1} h^{2}} \u9593\u306b\u30d0\u30a4\u30b8\u30a7\u30af\u30b7\u30e7\u30f3\u3092\u8a98\u5c0e\u3057\u307e\u3059 p s l \uff08 2 \u3001 r \uff09\uff09 {displaystyle psl\uff082\u3001mathbb {r}\uff09} \u3068 t 1h 2{displaystyle t^{1} h^{2}} \u3002\u306e\u52b9\u679c\u3092\u8003\u616e\u3057\u307e\u3059 p s l \uff08 2 \u3001 r \uff09\uff09 {displaystyle psl\uff082\u3001mathbb {r}\uff09} \u306e\u4e0a t 1h 2= p s l \uff08 2 \u3001 r \uff09\uff09 {displaystyle t^{1} h^{2} = psl\uff082\u3001mathbb {r}\uff09} \u5de6\u7ffc\u52b9\u679c\u3068\u3057\u3066\u3002\u305d\u306e\u5f8c\u3001\u6e2c\u5730\u5ddd\u304c\u5bfe\u5fdc\u3057\u307e\u3059 \u30d5\u30a1\u30a4 t{displaystyle phi _ {t}} \u306e\u6cd5\u7684\u52b9\u679c \uff08 et00e\u2212t\uff09\uff09 {displaystyle left\uff08{begin {array} {cc} e^{t}\uff060 \\ 0\uff06e^{ –  t} end {array}}\u53f3\uff09} \u306e\u4e0a p s l \uff08 2 \u3001 r \uff09\uff09 {displaystyle psl\uff082\u3001mathbb {r}\uff09} \u3002\u6e2c\u5730\u7dda\u5ddd\u306e\u5b89\u5b9a\u3057\u305f\u4e0d\u5b89\u5b9a\u306a\u30de\u30cb\u30db\u30fc\u30eb\u30c9\u306f\u3001\u30db\u30ed\u30b5\u30a4\u30af\u30eb\u3078\u306e\u30e6\u30cb\u30c3\u30c8\u30ed\u30c3\u30c9\u30d0\u30f3\u30c9\u30eb\u306e\u5236\u9650\u3067\u3042\u308a\u3001\u305d\u308c\u3089\u306f\u4e8c\u6b21\u30af\u30e9\u30b9\u306e\u30af\u30e9\u30b9\u3088\u308a\u3082\u4ee3\u6570\u7684\u306b\u8aac\u660e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 n += { (1n01):n\u2208R} {displaystyle n^{+} = left {left\uff08{begin {array} {cc} 1\uff06n \\ 0\uff061end {array}}\u53f3\uff09\uff1anin mathbb {r}\u53f3}}}} \u307e\u305f\u3002 n \u2212= { (10n1):n\u2208R} {displaystyle n^{ – } = left {left\uff08{begin {array} {cc} 1\uff060 \\ n\uff061end {array}}\u53f3\uff09\uff1anin mathbb {r}\u53f3}}}} \u3002 \u30d1\u30c8\u30ea\u30c3\u30af\u30fb\u30a8\u30d9\u30e9\u30a4\u30f3\uff1a 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