. "\u30D5\u30D3\u30CB\u30FB\u30B9\u30BF\u30C7\u30A3\u8A08\u91CF(Fubini\u2013Study metric)\u306F\u3001\u5C04\u5F71\u30D2\u30EB\u30D9\u30EB\u30C8\u7A7A\u9593\u4E0A\u306E\u30B1\u30FC\u30E9\u30FC\u8A08\u91CF\u3067\u3042\u308B\u3002\u3064\u307E\u308A\u3001\u8907\u7D20\u5C04\u5F71\u7A7A\u9593 CPn \u304C\u30A8\u30EB\u30DF\u30FC\u30C8\u5F62\u5F0F\u3092\u6301\u3064\u3053\u3068\u3092\u8A00\u3046\u3002\u3053\u306E\u8A08\u91CF\u306F\u3001\u3082\u3068\u3082\u3068\u306F1904\u5E74\u30681905\u5E74\u306B\u30B0\u30A4\u30C9\u30FB\u30D5\u30D3\u30CB(Guido Fubini)\u3068(Eduard Study)\u304C\u8A18\u8FF0\u3057\u305F\u3082\u306E\u3067\u3042\u3063\u305F\u3002 \u30D9\u30AF\u30C8\u30EB\u7A7A\u9593 Cn+1 \u306E\u30A8\u30EB\u30DF\u30FC\u30C8\u5F62\u5F0F\u306F\u3001GL(n+1,C) \u306E\u4E2D\u306E\u30E6\u30CB\u30BF\u30EA\u90E8\u5206\u7FA4 U(n+1) \u3092\u5B9A\u7FA9\u3059\u308B\u3002\u30D5\u30D3\u30CB\u30FB\u30B9\u30BF\u30C7\u30A3\u8A08\u91CF\u306F\u3001U(n+1) \u4F5C\u7528\u306E\u4E0B\u3067\u306E\u4E0D\u5909\u6027\uFF08\u30B9\u30B1\u30FC\u30EA\u30F3\u30B0\u306B\u5BFE\u3057\u3066\uFF09\u306B\u3088\u308A\u5DEE\u7570\u3092\u540C\u4E00\u8996\u3059\u308B\u3068\u6C7A\u5B9A\u3057\u3001\u7B49\u8CEA\u6027\u3092\u6301\u3064\u3002\u30D5\u30D3\u30CB\u30FB\u30B9\u30BF\u30C7\u30A3\u8A08\u91CF\u3092\u6301\u3064 CPn \u306F\u3001\uFF08\u30B9\u30B1\u30FC\u30EA\u30F3\u30B0\u3092\u6E21\u308B\uFF09(symmetric space)\u3067\u3042\u308B\u3002\u7279\u306B\u3001\u8A08\u91CF\u306E\u6B63\u898F\u5316\u306F\u3001\u30B9\u30B1\u30FC\u30EA\u30F3\u30B0\u306E\u9069\u7528\u306B\u4F9D\u5B58\u3059\u308B\u3002\u30EA\u30FC\u30DE\u30F3\u5E7E\u4F55\u5B66\u306B\u304A\u3044\u3066\u306F\u3001\u6B63\u898F\u5316\u3055\u308C\u305F\u8A08\u91CF\u3092\u4F7F\u3046\u3053\u3068\u304C\u3067\u304D\u308B\u306E\u3067\u3001(2n + 1) \u6B21\u5143\u7403\u9762\u4E0A\u306E\u30D5\u30D3\u30CB\u30FB\u30B9\u30BF\u30C7\u30A3\u8A08\u91CF\u306F\u3001\u5358\u7D14\u306B\u6A19\u6E96\u306E\u8A08\u91CF\u3068\u95A2\u9023\u4ED8\u3051\u3089\u308C\u308B\u3002\u4EE3\u6570\u5E7E\u4F55\u5B66\u3067\u306F\u3001\u6B63\u898F\u5316\u3092\u4F7F\u3044\u3001CPn \u3092\u30DB\u30C3\u30B8\u591A\u69D8\u4F53\u3068\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002"@ja . "\u5728\u6570\u5B66\u4E2D\uFF0C\u5BCC\u6BD4\u5C3C\u2013\u65BD\u56FE\u8FEA\u5EA6\u91CF\uFF08Fubini\u2013Study metric\uFF09\u662F\u4E0A\u4E00\u4E2A\u51EF\u52D2\u5EA6\u91CF\u3002\u6240\u8C13\u5C04\u5F71\u5E0C\u5C14\u4F2F\u7279\u7A7A\u95F4\u5373\u8D4B\u4E88\u4E86\u57C3\u5C14\u7C73\u7279\u5F62\u5F0F\u7684 CPn\u3002\u8FD9\u4E2A\u5EA6\u91CF\u6700\u5148\u7531\u572D\u591A\u00B7\u5BCC\u6BD4\u5C3C\u4E0E\u57281904\u5E74\u4E0E1905\u5E74\u63CF\u8FF0\u3002 \u5411\u91CF\u7A7A\u95F4 Cn+1 \u4E0A\u4E00\u4E2A\u57C3\u5C14\u7C73\u7279\u5F62\u5F0F\u5B9A\u4E49\u4E86 GL(n+1,C) \u4E2D\u4E00\u4E2A\u9149\u5B50\u7FA4 U(n+1)\u3002\u4E00\u4E2A\u5BCC\u6BD4\u5C3C\u2013\u65BD\u56FE\u8FEA\u5EA6\u91CF\u5728\u5DEE\u4E00\u4E2A\u4F4D\u4F3C\uFF08\u6574\u4F53\u7F29\u653E\uFF09\u7684\u610F\u4E49\u4E0B\u7531\u8FD9\u6837\u4E00\u4E2A U(n+1) \u4F5C\u7528\u4E0B\u7684\u4E0D\u53D8\u6027\u51B3\u5B9A\uFF1B\u4ECE\u800C\u662F\u9F50\u6027\u7684\u3002\u8D4B\u4E88\u8FD9\u6837\u4E00\u4E2A\u5BCC\u6BD4\u5C3C\u2013\u65BD\u56FE\u8FEA\u5EA6\u91CF\u540E\uFF0CCPn \u662F\u4E00\u4E2A\u3002\u5EA6\u91CF\u7684\u7279\u5B9A\u6B63\u89C4\u5316\u4E0E(2n+1)-\u7403\u9762\u4E0A\u7684\u6807\u51C6\u5EA6\u91CF\u6709\u5173\u3002\u5728\u4EE3\u6570\u51E0\u4F55\u4E2D\uFF0C\u5229\u7528\u4E00\u4E2A\u6B63\u89C4\u5316\u4F7F CPn \u6210\u4E3A\u4E00\u4E2A\u3002"@zh . . . . . . "Onishchik"@en . . . . "\uC218\uD559\uC5D0\uC11C \uD478\uBE44\uB2C8-\uC288\uD22C\uB514 \uACC4\uB7C9(Fubini\u2013Study metric)\uC740 \uBCF5\uC18C\uC218 \uC0AC\uC601 \uACF5\uAC04 \uC5D0 \uC8FC\uC5B4\uC9C0\uB294 \uCF08\uB7EC \uACC4\uB7C9\uC774\uB2E4."@ko . . . . "\u041C\u0435\u0442\u0440\u0438\u043A\u0430 \u0424\u0443\u0431\u0438\u043D\u0438 \u2014 \u0428\u0442\u0443\u0434\u0438"@ru . . . . "Fubini\u2013Study metric"@en . . . "\u30D5\u30D3\u30CB\u30FB\u30B9\u30BF\u30C7\u30A3\u8A08\u91CF"@ja . "In mathematics, the Fubini\u2013Study metric is a K\u00E4hler metric on projective Hilbert space, that is, on a complex projective space CPn endowed with a Hermitian form. This metric was originally described in 1904 and 1905 by Guido Fubini and Eduard Study. A Hermitian form in (the vector space) Cn+1 defines a unitary subgroup U(n+1) in GL(n+1,C). A Fubini\u2013Study metric is determined up to homothety (overall scaling) by invariance under such a U(n+1) action; thus it is homogeneous. Equipped with a Fubini\u2013Study metric, CPn is a symmetric space. The particular normalization on the metric depends on the application. In Riemannian geometry, one uses a normalization so that the Fubini\u2013Study metric simply relates to the standard metric on the (2n+1)-sphere. In algebraic geometry, one uses a normalization making CPn a Hodge manifold."@en . . . . . "2574486"^^ . . . . . "\u30D5\u30D3\u30CB\u30FB\u30B9\u30BF\u30C7\u30A3\u8A08\u91CF(Fubini\u2013Study metric)\u306F\u3001\u5C04\u5F71\u30D2\u30EB\u30D9\u30EB\u30C8\u7A7A\u9593\u4E0A\u306E\u30B1\u30FC\u30E9\u30FC\u8A08\u91CF\u3067\u3042\u308B\u3002\u3064\u307E\u308A\u3001\u8907\u7D20\u5C04\u5F71\u7A7A\u9593 CPn \u304C\u30A8\u30EB\u30DF\u30FC\u30C8\u5F62\u5F0F\u3092\u6301\u3064\u3053\u3068\u3092\u8A00\u3046\u3002\u3053\u306E\u8A08\u91CF\u306F\u3001\u3082\u3068\u3082\u3068\u306F1904\u5E74\u30681905\u5E74\u306B\u30B0\u30A4\u30C9\u30FB\u30D5\u30D3\u30CB(Guido Fubini)\u3068(Eduard Study)\u304C\u8A18\u8FF0\u3057\u305F\u3082\u306E\u3067\u3042\u3063\u305F\u3002 \u30D9\u30AF\u30C8\u30EB\u7A7A\u9593 Cn+1 \u306E\u30A8\u30EB\u30DF\u30FC\u30C8\u5F62\u5F0F\u306F\u3001GL(n+1,C) \u306E\u4E2D\u306E\u30E6\u30CB\u30BF\u30EA\u90E8\u5206\u7FA4 U(n+1) \u3092\u5B9A\u7FA9\u3059\u308B\u3002\u30D5\u30D3\u30CB\u30FB\u30B9\u30BF\u30C7\u30A3\u8A08\u91CF\u306F\u3001U(n+1) \u4F5C\u7528\u306E\u4E0B\u3067\u306E\u4E0D\u5909\u6027\uFF08\u30B9\u30B1\u30FC\u30EA\u30F3\u30B0\u306B\u5BFE\u3057\u3066\uFF09\u306B\u3088\u308A\u5DEE\u7570\u3092\u540C\u4E00\u8996\u3059\u308B\u3068\u6C7A\u5B9A\u3057\u3001\u7B49\u8CEA\u6027\u3092\u6301\u3064\u3002\u30D5\u30D3\u30CB\u30FB\u30B9\u30BF\u30C7\u30A3\u8A08\u91CF\u3092\u6301\u3064 CPn \u306F\u3001\uFF08\u30B9\u30B1\u30FC\u30EA\u30F3\u30B0\u3092\u6E21\u308B\uFF09(symmetric space)\u3067\u3042\u308B\u3002\u7279\u306B\u3001\u8A08\u91CF\u306E\u6B63\u898F\u5316\u306F\u3001\u30B9\u30B1\u30FC\u30EA\u30F3\u30B0\u306E\u9069\u7528\u306B\u4F9D\u5B58\u3059\u308B\u3002\u30EA\u30FC\u30DE\u30F3\u5E7E\u4F55\u5B66\u306B\u304A\u3044\u3066\u306F\u3001\u6B63\u898F\u5316\u3055\u308C\u305F\u8A08\u91CF\u3092\u4F7F\u3046\u3053\u3068\u304C\u3067\u304D\u308B\u306E\u3067\u3001(2n + 1) \u6B21\u5143\u7403\u9762\u4E0A\u306E\u30D5\u30D3\u30CB\u30FB\u30B9\u30BF\u30C7\u30A3\u8A08\u91CF\u306F\u3001\u5358\u7D14\u306B\u6A19\u6E96\u306E\u8A08\u91CF\u3068\u95A2\u9023\u4ED8\u3051\u3089\u308C\u308B\u3002\u4EE3\u6570\u5E7E\u4F55\u5B66\u3067\u306F\u3001\u6B63\u898F\u5316\u3092\u4F7F\u3044\u3001CPn \u3092\u30DB\u30C3\u30B8\u591A\u69D8\u4F53\u3068\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002"@ja . . . . . . . . . "\uC218\uD559\uC5D0\uC11C \uD478\uBE44\uB2C8-\uC288\uD22C\uB514 \uACC4\uB7C9(Fubini\u2013Study metric)\uC740 \uBCF5\uC18C\uC218 \uC0AC\uC601 \uACF5\uAC04 \uC5D0 \uC8FC\uC5B4\uC9C0\uB294 \uCF08\uB7EC \uACC4\uB7C9\uC774\uB2E4."@ko . . . "27517"^^ . . . . . . . . . . . . . . . "\u5BCC\u6BD4\u5C3C\u2013\u65BD\u56FE\u8FEA\u5EA6\u91CF"@zh . "En g\u00E9om\u00E9trie diff\u00E9rentielle, la m\u00E9trique de Fubini-Study est une m\u00E9trique k\u00E4hl\u00E9rienne sur l'espace projectif complexe CPn En m\u00E9canique quantique, les physiciens ont coutume de l'appeler la sph\u00E8re de Bloch. \n* Portail de la g\u00E9om\u00E9trie"@fr . . . "Fubini\u2013Study metric"@en . . "M\u00E9trique de Fubini-Study"@fr . . . . . . . . . . . . . . . . . . . . . . . . . "1113955404"^^ . . . "A.L."@en . . . . . . . "2001"^^ . . . . . . . . . . . . . "In mathematics, the Fubini\u2013Study metric is a K\u00E4hler metric on projective Hilbert space, that is, on a complex projective space CPn endowed with a Hermitian form. This metric was originally described in 1904 and 1905 by Guido Fubini and Eduard Study."@en . . . . "En g\u00E9om\u00E9trie diff\u00E9rentielle, la m\u00E9trique de Fubini-Study est une m\u00E9trique k\u00E4hl\u00E9rienne sur l'espace projectif complexe CPn En m\u00E9canique quantique, les physiciens ont coutume de l'appeler la sph\u00E8re de Bloch. \n* Portail de la g\u00E9om\u00E9trie"@fr . . "F/f041860"@en . . . . . . . . . . . . . . "\u5728\u6570\u5B66\u4E2D\uFF0C\u5BCC\u6BD4\u5C3C\u2013\u65BD\u56FE\u8FEA\u5EA6\u91CF\uFF08Fubini\u2013Study metric\uFF09\u662F\u4E0A\u4E00\u4E2A\u51EF\u52D2\u5EA6\u91CF\u3002\u6240\u8C13\u5C04\u5F71\u5E0C\u5C14\u4F2F\u7279\u7A7A\u95F4\u5373\u8D4B\u4E88\u4E86\u57C3\u5C14\u7C73\u7279\u5F62\u5F0F\u7684 CPn\u3002\u8FD9\u4E2A\u5EA6\u91CF\u6700\u5148\u7531\u572D\u591A\u00B7\u5BCC\u6BD4\u5C3C\u4E0E\u57281904\u5E74\u4E0E1905\u5E74\u63CF\u8FF0\u3002 \u5411\u91CF\u7A7A\u95F4 Cn+1 \u4E0A\u4E00\u4E2A\u57C3\u5C14\u7C73\u7279\u5F62\u5F0F\u5B9A\u4E49\u4E86 GL(n+1,C) \u4E2D\u4E00\u4E2A\u9149\u5B50\u7FA4 U(n+1)\u3002\u4E00\u4E2A\u5BCC\u6BD4\u5C3C\u2013\u65BD\u56FE\u8FEA\u5EA6\u91CF\u5728\u5DEE\u4E00\u4E2A\u4F4D\u4F3C\uFF08\u6574\u4F53\u7F29\u653E\uFF09\u7684\u610F\u4E49\u4E0B\u7531\u8FD9\u6837\u4E00\u4E2A U(n+1) \u4F5C\u7528\u4E0B\u7684\u4E0D\u53D8\u6027\u51B3\u5B9A\uFF1B\u4ECE\u800C\u662F\u9F50\u6027\u7684\u3002\u8D4B\u4E88\u8FD9\u6837\u4E00\u4E2A\u5BCC\u6BD4\u5C3C\u2013\u65BD\u56FE\u8FEA\u5EA6\u91CF\u540E\uFF0CCPn \u662F\u4E00\u4E2A\u3002\u5EA6\u91CF\u7684\u7279\u5B9A\u6B63\u89C4\u5316\u4E0E(2n+1)-\u7403\u9762\u4E0A\u7684\u6807\u51C6\u5EA6\u91CF\u6709\u5173\u3002\u5728\u4EE3\u6570\u51E0\u4F55\u4E2D\uFF0C\u5229\u7528\u4E00\u4E2A\u6B63\u89C4\u5316\u4F7F CPn \u6210\u4E3A\u4E00\u4E2A\u3002"@zh . . . . . . "\uD478\uBE44\uB2C8-\uC288\uD22C\uB514 \uACC4\uB7C9"@ko . . . . . .