[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/5502#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/5502","headline":"\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53 – Wikipedia","name":"\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53 – Wikipedia","description":"\u539f\u6587\u3068\u6bd4\u3079\u305f\u7d50\u679c\u3001\u3053\u306e\u8a18\u4e8b\u306b\u306f\u591a\u6570\uff08\u5c11\u306a\u304f\u3068\u30825\u500b\u4ee5\u4e0a\uff09\u306e\u8aa4\u8a33\u304c\u3042\u308b\u3053\u3068\u304c\u5224\u660e\u3057\u3066\u3044\u307e\u3059\u3002\u60c5\u5831\u306e\u5229\u7528\u306b\u306f\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u6b63\u78ba\u306a\u8868\u73fe\u306b\u6539\u8a33\u3067\u304d\u308b\u65b9\u3092\u6c42\u3081\u3066\u3044\u307e\u3059\u3002 \u5fae\u5206\u5e7e\u4f55\u5b66\u306b\u304a\u3044\u3066\u3001\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53 (pseudo-Riemannian manifold)[1][2]\uff08\u307e\u305f\u3001\u534a\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53 (semi-Riemannian manifold) \u3068\u3082\u3044\u3046\uff09\u306f\u3001\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u4e00\u822c\u5316\u3067\u3042\u308a\u3001\u305d\u3053\u3067\u306f\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u304c\u5fc5\u305a\u3057\u3082\u6b63\u5b9a\u5024\u53cc\u7dda\u578b\u5f62\u5f0f\uff08\u82f1\u8a9e\u7248\uff09\u3067\u306a\u3044\u3053\u3068\u3082\u3042\u308b\u3002\u4ee3\u308f\u3063\u3066\u3001\u975e\u9000\u5316\u3068\u3044\u3046\u3088\u308a\u5f31\u3044\u6761\u4ef6\u304c\u3001\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u3078\u5c0e\u5165\u3055\u308c\u308b\u3002 \u4e00\u822c\u76f8\u5bfe\u8ad6\u3067\u6975\u3081\u3066\u91cd\u8981\u306a\u591a\u69d8\u4f53\u3068\u3057\u3066\u3001\u30ed\u30fc\u30ec\u30f3\u30c4\u591a\u69d8\u4f53 (Lorentzian manifold) \u304c\u3042\u308a\u3001\u305d\u3053\u3067\u306f\u3001\u4e00\u3064\u306e\u6b21\u5143\u304c\u4ed6\u306e\u6b21\u5143\u3068\u306f\u53cd\u5bfe\u306e\u7b26\u53f7\u3092\u6301\u3063\u3066\u3044\u308b\u3002\u3053\u306e\u3053\u3068\u306f\u3001\u63a5\u30d9\u30af\u30c8\u30eb\u304c\u6642\u9593\u7684\u3001\u5149\u7684\u3001\u7a7a\u9593\u7684[3] \u3078\u3068\u5206\u985e\u3055\u308c\u308b\u3002\u6642\u7a7a\u306f 4\u6b21\u5143\u30ed\u30fc\u30ec\u30f3\u30c4\u591a\u69d8\u4f53\u3068\u3057\u3066\u30e2\u30c7\u30eb\u5316\u3055\u308c\u308b\u3002 Table of Contents \u591a\u69d8\u4f53[\u7de8\u96c6]\u63a5\u7a7a\u9593\u3068\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb[\u7de8\u96c6]\u8a08\u91cf\u7b26\u53f7[\u7de8\u96c6]\u30ed\u30fc\u30ec\u30f3\u30c4\u591a\u69d8\u4f53[\u7de8\u96c6]\u7269\u7406\u5b66\u3078\u306e\u5fdc\u7528[\u7de8\u96c6]\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u6027\u8cea[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6] \u591a\u69d8\u4f53[\u7de8\u96c6] \u5fae\u5206\u5e7e\u4f55\u5b66\u306b\u304a\u3044\u3066\u3001\u5fae\u5206\u53ef\u80fd\u591a\u69d8\u4f53\u306f\u3001\u5c40\u6240\u7684\u306b\u306f\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u3068\u540c\u3058\u7a7a\u9593\u3067\u3042\u308b\u3002n-\u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u3067\u306f\u3001\u4efb\u610f\u306e\u70b9\u304c n","datePublished":"2020-04-30","dateModified":"2020-04-30","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?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:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/b\/b2\/Blue_question_mark.svg\/30px-Blue_question_mark.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/b\/b2\/Blue_question_mark.svg\/30px-Blue_question_mark.svg.png","height":"30","width":"30"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/5502","about":["Wiki"],"wordCount":3324,"articleBody":"\u539f\u6587\u3068\u6bd4\u3079\u305f\u7d50\u679c\u3001\u3053\u306e\u8a18\u4e8b\u306b\u306f\u591a\u6570\uff08\u5c11\u306a\u304f\u3068\u30825\u500b\u4ee5\u4e0a\uff09\u306e\u8aa4\u8a33\u304c\u3042\u308b\u3053\u3068\u304c\u5224\u660e\u3057\u3066\u3044\u307e\u3059\u3002\u60c5\u5831\u306e\u5229\u7528\u306b\u306f\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u6b63\u78ba\u306a\u8868\u73fe\u306b\u6539\u8a33\u3067\u304d\u308b\u65b9\u3092\u6c42\u3081\u3066\u3044\u307e\u3059\u3002\u5fae\u5206\u5e7e\u4f55\u5b66\u306b\u304a\u3044\u3066\u3001\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53 (pseudo-Riemannian manifold)[1][2]\uff08\u307e\u305f\u3001\u534a\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53 (semi-Riemannian manifold) \u3068\u3082\u3044\u3046\uff09\u306f\u3001\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u4e00\u822c\u5316\u3067\u3042\u308a\u3001\u305d\u3053\u3067\u306f\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u304c\u5fc5\u305a\u3057\u3082\u6b63\u5b9a\u5024\u53cc\u7dda\u578b\u5f62\u5f0f\uff08\u82f1\u8a9e\u7248\uff09\u3067\u306a\u3044\u3053\u3068\u3082\u3042\u308b\u3002\u4ee3\u308f\u3063\u3066\u3001\u975e\u9000\u5316\u3068\u3044\u3046\u3088\u308a\u5f31\u3044\u6761\u4ef6\u304c\u3001\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u3078\u5c0e\u5165\u3055\u308c\u308b\u3002\u4e00\u822c\u76f8\u5bfe\u8ad6\u3067\u6975\u3081\u3066\u91cd\u8981\u306a\u591a\u69d8\u4f53\u3068\u3057\u3066\u3001\u30ed\u30fc\u30ec\u30f3\u30c4\u591a\u69d8\u4f53 (Lorentzian manifold) \u304c\u3042\u308a\u3001\u305d\u3053\u3067\u306f\u3001\u4e00\u3064\u306e\u6b21\u5143\u304c\u4ed6\u306e\u6b21\u5143\u3068\u306f\u53cd\u5bfe\u306e\u7b26\u53f7\u3092\u6301\u3063\u3066\u3044\u308b\u3002\u3053\u306e\u3053\u3068\u306f\u3001\u63a5\u30d9\u30af\u30c8\u30eb\u304c\u6642\u9593\u7684\u3001\u5149\u7684\u3001\u7a7a\u9593\u7684[3] \u3078\u3068\u5206\u985e\u3055\u308c\u308b\u3002\u6642\u7a7a\u306f 4\u6b21\u5143\u30ed\u30fc\u30ec\u30f3\u30c4\u591a\u69d8\u4f53\u3068\u3057\u3066\u30e2\u30c7\u30eb\u5316\u3055\u308c\u308b\u3002Table of Contents\u591a\u69d8\u4f53[\u7de8\u96c6]\u63a5\u7a7a\u9593\u3068\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb[\u7de8\u96c6]\u8a08\u91cf\u7b26\u53f7[\u7de8\u96c6]\u30ed\u30fc\u30ec\u30f3\u30c4\u591a\u69d8\u4f53[\u7de8\u96c6]\u7269\u7406\u5b66\u3078\u306e\u5fdc\u7528[\u7de8\u96c6]\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u6027\u8cea[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u591a\u69d8\u4f53[\u7de8\u96c6]\u5fae\u5206\u5e7e\u4f55\u5b66\u306b\u304a\u3044\u3066\u3001\u5fae\u5206\u53ef\u80fd\u591a\u69d8\u4f53\u306f\u3001\u5c40\u6240\u7684\u306b\u306f\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u3068\u540c\u3058\u7a7a\u9593\u3067\u3042\u308b\u3002n-\u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u3067\u306f\u3001\u4efb\u610f\u306e\u70b9\u304c n \u500b\u306e\u5b9f\u6570\u306b\u3088\u308a\u7279\u5b9a\u3055\u308c\u308b\u3002\u3053\u308c\u3089\u3092\u70b9\u306e\u5ea7\u6a19\u3068\u547c\u3076\u3002  n-\u6b21\u5143\u5fae\u5206\u53ef\u80fd\u591a\u69d8\u4f53\u306f\u3001n-\u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u306e\u4e00\u822c\u5316\u3067\u3042\u308b\u3002\u591a\u69d8\u4f53\u3067\u306f\u3001\u5c40\u6240\u7684\u306b\u5ea7\u6a19\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u306e\u3053\u3068\u306f\u5ea7\u6a19\u306e\u8cbc\u308a\u5408\u308f\u305b(coordinate patch)\u304c\u9054\u6210\u3067\u304d\u3066\u3001\u591a\u69d8\u4f53\u306e\u90e8\u5206\u96c6\u5408\u306f n-\u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u3078\u5199\u50cf\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u8a73\u7d30\u306f\u3001\u591a\u69d8\u4f53, \u5fae\u5206\u53ef\u80fd\u591a\u69d8\u4f53, \u5ea7\u6a19\u306e\u8cbc\u308a\u5408\u308f\u305b(coordinate patch)\u3092\u53c2\u7167\u3002\u63a5\u7a7a\u9593\u3068\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb[\u7de8\u96c6]\u63a5\u7a7a\u9593\u306f\u3001n \u6b21\u5143\u5fae\u5206\u53ef\u80fd\u591a\u69d8\u4f53 M \u306e\u5404\u3005\u306e\u70b9 p \u306b\u4ed8\u968f\u3057\u3001TpM \u3068\u66f8\u304b\u308c\u308b\u3002\u63a5\u7a7a\u9593\u306f\u3001\u305d\u306e\u5143\u304c\u70b9 p \u3092\u901a\u308b\u66f2\u7dda\u306e\u540c\u5024\u985e\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b n \u6b21\u5143\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3067\u3042\u308b\u3002\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306f\u975e\u9000\u5316\u3067\u3042\u308a\u3001\u6ed1\u3089\u304b\u3067\u3001\u5bfe\u79f0\u6027\u3092\u6301\u3064\u53cc\u7dda\u5f62\u5199\u50cf\u3067\u3001\u591a\u69d8\u4f53\u306e\u5404\u3005\u306e\u63a5\u7a7a\u9593\u3067\u306e\u63a5\u30d9\u30af\u30c8\u30eb\u306e\u30da\u30a2\u306b\u5b9f\u6570\u3092\u5272\u308a\u5f53\u3066\u308b\u3002\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u3092 g \u3068\u66f8\u304f\u3068\u3001\u3053\u308c\u306f  g:TpM\u00d7TpM\u2192R.{displaystyle gcolon T_{p}Mtimes T_{p}Mto mathbb {R} .}\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u5199\u50cf\u306f\u5bfe\u79f0\u7684\u3067\u53cc\u7dda\u5f62\u3067\u3042\u308b\u306e\u3067\u3001X,Y,Z\u2208TpM{displaystyle scriptstyle X,Y,Zin T_{p}M} \u304c\u70b9 p \u3067\u591a\u69d8\u4f53 M \u306e\u63a5\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308c\u3070\u3001\u4efb\u610f\u306e\u5b9f\u6570   a\u2208R{displaystyle scriptstyle ain mathbb {R} } \u306b\u5bfe\u3057\u3001g(X,Y)=g(Y,X){displaystyle ,g(X,Y)=g(Y,X)}g(aX+Y,Z)=ag(X,Z)+g(Y,Z){displaystyle ,g(aX+Y,Z)=ag(X,Z)+g(Y,Z)}\u3068\u306a\u308b\u3002g \u304c\u975e\u9000\u5316\u3067\u3042\u308b\u3053\u3068\u306f\u3001\u3059\u3079\u3066\u306e Y\u2208TpM{displaystyle Yin T_{p}M} \u306b\u5bfe\u3057 g(X,Y)=0{displaystyle ,g(X,Y)=0} \u3068\u306a\u308b\u3088\u3046\u306a\uff080 \u3067\u306f\u306a\u3044\uff09X\u2208TpM{displaystyle Xin T_{p}M} \u306f\u5b58\u5728\u3057\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u8a08\u91cf\u7b26\u53f7[\u7de8\u96c6]n-\u6b21\u5143\u5b9f\u591a\u69d8\u4f53\u4e0a\u306e\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb g \u304c\u4e0e\u3048\u3089\u308c\u308b\u3068\u3001\u4efb\u610f\u306e\u76f4\u4ea4\u57fa\u5e95\uff08\u82f1\u8a9e\u7248\uff09\u306e\u305d\u308c\u305e\u308c\u306e\u30d9\u30af\u30c8\u30eb\u3078\u9069\u7528\u3055\u308c\u305f\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306b\u4ed8\u968f\u3059\u308b\u4e8c\u6b21\u5f62\u5f0f q(x) = g(x,x) \u304c n \u500b\u306e\u5b9f\u6570\u5024\u3067\u8868\u3055\u308c\u308b\u3002\u4e8c\u6b21\u5f62\u5f0f\u306e\u6163\u6027\u6cd5\u5247\u306b\u3088\u308a\u3001\u3053\u306e\u65b9\u6cd5\u3067\u8868\u3055\u308c\u305f\u5404\u3005\u306e\u6b63\u3001\u8ca0\u3001\u96f6\u306e\u5024\u306e\u6570\u306f\u3001\u76f4\u4ea4\u57fa\u5e95\u306e\u9078\u629e\u3068\u306f\u72ec\u7acb\u306a\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306b\u5bfe\u3057\u3066\u4e0d\u5909\u3067\u3042\u308b\u3002\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306e\u8a08\u91cf\u7b26\u53f7 (signature) (p, q, r) \u306f\u305d\u308c\u305e\u308c\u306e\u9806\u756a\u901a\u308a\u306e\u6570\u5024\u3092\u4e0e\u3048\u308b\u3002\u975e\u9000\u5316\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306f r = 0 \u3067\u3042\u308a\u3001\u7b26\u53f7\u306f p + q = n \u306e\u3068\u304d\u306f\u3001(p, q) \u3068\u66f8\u304b\u308c\u308b\u3002\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53 (pseudo-Riemannian manifold) (M,g){displaystyle (M,g)} \u306f\u3001\u975e\u9000\u5316\u3067\u6ed1\u3089\u304b\u306a\u5bfe\u79f0\u306a\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb g \u3092\u6301\u3064\u5fae\u5206\u53ef\u80fd\u591a\u69d8\u4f53 M \u3067\u3042\u308b\u3002\u305d\u306e\u3088\u3046\u306a\u8a08\u91cf\u3092\u3001\u64ec\u30ea\u30fc\u30de\u30f3\u8a08\u91cf (pseudo-Riemannian metric) \u3068\u547c\u3073\u3001\u305d\u306e\u5024\u306f\u3001\u6b63\u3001\u8ca0\u3001\u96f6\u3068\u306a\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u64ec\u30ea\u30fc\u30de\u30f3\u8a08\u91cf\u306e\u7b26\u53f7\u306f\u3001(p,\u2009q) \u3067\u3042\u308a\u3001p \u3068 q \u306f\u975e\u8ca0\u3067\u3042\u308b\u3002\u30ed\u30fc\u30ec\u30f3\u30c4\u591a\u69d8\u4f53[\u7de8\u96c6]\u30ed\u30fc\u30ec\u30f3\u30c4\u591a\u69d8\u4f53 (Lorentzian manifold) \u306f\u3001\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u7279\u5225\u306b\u91cd\u8981\u306a\u4f8b\u3067\u3001\u305d\u3053\u3067\u306f\u8a08\u91cf\u306e\u7b26\u53f7\u304c (1,\u2009\u22121, \u2026 , \u22121)) (\u3068\u304d\u306b\u306f\u3001 (\u22121, \u2026 , \u22121,\u20091) \u306e\u3053\u3068\u3082\u3042\u308b\u3002\u300c\u7b26\u53f7\u306e\u898f\u7d04\u300d\u3092\u53c2\u7167) \u3067\u3042\u308b\u3002\u305d\u306e\u3088\u3046\u306a\u8a08\u91cf\u3092\u30ed\u30fc\u30ec\u30f3\u30c4\u8a08\u91cf\u3068\u547c\u3076\u3002\u30ed\u30fc\u30ec\u30f3\u30c4\u8a08\u91cf\u306f\u3001\u7269\u7406\u5b66\u8005\u30d8\u30f3\u30c9\u30ea\u30c3\u30af\u30fb\u30ed\u30fc\u30ec\u30f3\u30c4 (Hendrik Lorentz) \u306b\u3061\u306a\u3093\u3067\u3044\u308b\u3002\u7269\u7406\u5b66\u3078\u306e\u5fdc\u7528[\u7de8\u96c6]\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u5f8c\u306b\u7d9a\u3044\u3066\u3001\u30ed\u30fc\u30ec\u30f3\u30c4\u591a\u69d8\u4f53\u306f\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u6700\u3082\u91cd\u8981\u306a\u90e8\u5206\u3092\u306a\u3059\u3002\u30ed\u30fc\u30ec\u30f3\u30c4\u591a\u69d8\u4f53\u306f\u3001\u4e00\u822c\u76f8\u5bfe\u8ad6\u306e\u5fdc\u7528\u306b\u304a\u3044\u3066\u91cd\u8981\u3067\u3042\u308b\u3002\u4e00\u822c\u76f8\u5bfe\u8ad6\u306e\u539f\u7406\u7684\u306a\u57fa\u790e\u306f\u3001\u6642\u7a7a\u306f\u7b26\u53f7 (3,\u20091) \u3082\u3057\u304f\u306f\u3001\u540c\u3058\u3053\u3068\u3067\u3042\u308b\u304c\u3001(1,\u20093) \u3092\u6301\u3064 4\u6b21\u5143\u30ed\u30fc\u30ec\u30f3\u30c4\u591a\u69d8\u4f53\u3068\u3057\u3066\u30e2\u30c7\u30eb\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u6b63\u5b9a\u5024\u306e\u8a08\u91cf\u3092\u3082\u3064\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u3068\u306f\u7570\u306a\u308a\u3001(3, 1) \u3082\u3057\u304f\u306f (1, 3) \u306e\u7b26\u53f7\u306f\u3001\u63a5\u30d9\u30af\u30c8\u30eb\u3092\u6642\u9593\u7684\u3001\u5149\u7684\u3001\u7a7a\u9593\u7684\u3078\u5206\u985e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff08\u56e0\u679c\u5f8b\u3092\u53c2\u7167\uff09\u3002\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u6027\u8cea[\u7de8\u96c6]\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 Rn{displaystyle mathbb {R} ^{n}} \u304c\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u30e2\u30c7\u30eb\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u3001\u5e73\u5766\u306a\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u8a08\u91cf\u3092\u3082\u3064\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u7a7a\u9593 Rn\u22121,1{displaystyle mathbb {R} ^{n-1,1}} \u306f\u3001\u30ed\u30fc\u30ec\u30f3\u30c4\u591a\u69d8\u4f53\u306e\u30e2\u30c7\u30eb\u3067\u3042\u308b\u3002\u540c\u69d8\u306b\u3057\u3066\u3001\u7b26\u53f7 (p,\u2009q) \u306e\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u30e2\u30c7\u30eb\u7a7a\u9593\u306f\u3001Rp,q{displaystyle mathbb {R} ^{p,q}} \u3067\u3042\u308a\u3001\u305d\u306e\u8a08\u91cf\u306f\u3001g=dx12+\u22ef+dxp2\u2212dxp+12\u2212\u22ef\u2212dxp+q2{displaystyle g=dx_{1}^{2}+cdots +dx_{p}^{2}-dx_{p+1}^{2}-cdots -dx_{p+q}^{2}}\u3067\u3042\u308b\u3002\u30ea\u30fc\u30de\u30f3\u5e7e\u4f55\u5b66\u306e\u57fa\u672c\u7684\u306a\u5b9a\u7406\u306f\u3001\u64ec\u30ea\u30fc\u30de\u30f3\u7684\u3067\u3042\u308b\u5834\u5408\u306b\u4e00\u822c\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u7279\u306b\u3001\u30ea\u30fc\u30de\u30f3\u5e7e\u4f55\u5b66\u306e\u57fa\u672c\u5b9a\u7406\u306f\u3001\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306b\u5bfe\u3057\u3066\u3082\u540c\u69d8\u306b\u6210\u7acb\u3059\u308b\u3002\u3053\u306e\u3053\u3068\u306f\u3001\u4ed8\u968f\u3059\u308b\u66f2\u7387\u30c6\u30f3\u30bd\u30eb\u306b\u6cbf\u3063\u305f\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u4e0a\u306e\u30ec\u30f4\u30a3\u30fb\u30c1\u30f4\u30a3\u30bf\u63a5\u7d9a\u306b\u3064\u3044\u3066\u8a9e\u308b\u3053\u3068\u3092\u53ef\u80fd\u3068\u3059\u308b\u3002\u4ed6\u65b9\u3001\u30ea\u30fc\u30de\u30f3\u5e7e\u4f55\u5b66\u306e\u5b9a\u7406\u3067\u4e00\u822c\u306e\u5834\u5408\u306b\u306f\u6210\u308a\u7acb\u305f\u306a\u3044\u5b9a\u7406\u3082\u591a\u304f\u5b58\u5728\u3059\u308b\u3002\u305f\u3068\u3048\u3070\u3001\u3059\u3079\u3066\u306e\u6ed1\u3089\u304b\u306a\u591a\u69d8\u4f53\u306f\u4e0e\u3048\u3089\u308c\u305f\u7b26\u53f7\u3092\u3082\u3064\u64ec\u30ea\u30fc\u30de\u30f3\u8a08\u91cf\u3068\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306f\u6210\u7acb\u3057\u306a\u3044\u3002\u3053\u306e\u5834\u5408\u306b\u306f\u3001\u3042\u308b\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u306a\u969c\u5bb3\u304c\u5b58\u5728\u3059\u308b\u3002\u3055\u3089\u306b\u3001\uff08\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\uff09\u90e8\u5206\u591a\u69d8\u4f53\u304c\u5e38\u306b\u3001\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u69cb\u9020\u3092\u5f15\u304d\u7d99\u3050\u308f\u3051\u3067\u306f\u306a\u3044\u3002\u305f\u3068\u3048\u3070\u3001\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306f\u3001\u4efb\u610f\u306e\u5149\u7684\u306a\u66f2\u7dda\u4e0a\u306e\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306f 0 \u3068\u306a\u308b\u3002\u30af\u30ea\u30d5\u30c8\u30f3\u30fb\u30dd\u30fc\u30eb\u306e\u30c8\u30fc\u30e9\u30b9\uff08\u82f1\u8a9e\u7248\uff09(Clifton\u2013Pohl torus)\u306f\u3001\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3042\u308b\u304c\u5b8c\u5099\u3067\u306f\u306a\u3044\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u4f8b\u3092\u3082\u305f\u3089\u3057\u305f\u3002\u5b8c\u5099\u3067\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u4e0a\u3067\u306f\u6210\u7acb\u3059\u308b\u30db\u30c3\u30d7\u30fb\u30ea\u30ce\u30fc\u306e\u5b9a\u7406\uff08\u82f1\u8a9e\u7248\uff09\u306f\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53\u306e\u4e0a\u3067\u306f\u6210\u7acb\u3057\u306a\u3044[4]\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Benn, I.M.; Tucker, R.W. (1987), An introduction to Spinors and Geometry with Applications in Physics (First published 1987 ed.), Adam Hilger, ISBN\u00a00-85274-169-3\u00a0Bishop, Richard L.; Goldberg, Samuel I. (1968), Tensor Analysis on Manifolds (First Dover 1980 ed.), The Macmillan Company, ISBN\u00a00-486-64039-6\u00a0Chen, Bang-Yen (2011), Pseudo-Riemannian Geometry, [delta]-invariants and Applications, World Scientific Publisher, ISBN\u00a0978-981-4329-63-7\u00a0O’Neill, Barrett (1983), Semi-Riemannian Geometry With Applications to Relativity, Pure and Applied Mathematics, 103, Academic Press, ISBN\u00a09780080570570, http:\/\/books.google.com\/books?id=CGk1eRSjFIIC&pg=PA193\u00a0Vr\u0103nceanu, G.; Ro\u015fca, R. (1976), Introduction to Relativity and Pseudo-Riemannian Geometry, Bucarest: Editura Academiei Republicii Socialiste Rom\u00e2nia\u00a0."},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/5502#breadcrumbitem","name":"\u64ec\u30ea\u30fc\u30de\u30f3\u591a\u69d8\u4f53 – Wikipedia"}}]}]