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        "quote": "<span id=\"node-a-1622d8a957a18ab37c1cc938\" class=\"block-anchor\"></span>至此，我们一直让 $\\Gamma$ 保持任意。既然现在流形上已配有度量，我们就可以对联络可能取的形式施加合理的限制。我们要求度量 $g_{\\mu \\nu}$ 是<span class=\"concept-mention-pending\" id=\"bound-first-399085d93ba323ce9d28bc8d\" data-concept-identity=\"urn:uuid:0df7bc14-09d5-5ee4-8ec5-834ae827d0f3\" data-concept-role=\"first-mention\" data-concept-first-mention=\"true\" data-concept-navigation-schema=\"1\" data-concept-source-node=\"a-1622d8a957a18ab37c1cc938\" data-concept-identity-status=\"provisional\" data-concept-definition-status=\"mention\">协变常数</span>的，也就是说，若两个向量 $X$ 与 $Y$ 沿任意曲线作平行移动，则它们之间的<a class=\"concept-reference\" href=\"01-section-7-1.md#bound-definition-9094fd4d3ca4a94fdb8d5149\"><u class=\"concept-term\" id=\"bound-mention-c86c1498597fd1c1d12f0895\" data-concept-identity=\"urn:uuid:0a507b65-dfea-4bc8-ada8-442de630a818\" data-concept-role=\"discussion\" data-concept-first-mention=\"false\" data-concept-navigation-schema=\"1\" data-concept-source-node=\"a-1622d8a957a18ab37c1cc938\" data-concept-identity-status=\"formal\" data-concept-definition-status=\"mention\" data-concept-route=\"/concepts/by-id/0a507b65-dfea-4bc8-ada8-442de630a818\" title=\"查看本书定义\" data-concept-reference=\"bound-definition-9094fd4d3ca4a94fdb8d5149\" data-concept-reference-basis=\"definition\" data-concept-first-mention-target=\"/books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-01/02-section-1-2#bound-first-532258cd337fb2797da2dd95\">内积</u></a>在平行移动下保持不变。[在[例 7.1](02-section-7-2.md#example-7-1)中，我们已经假定了这一合理条件。]设 $V$ 为任意一条曲线上的切向量，而向量正是沿这条曲线作平行移动的。于是有",
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        "quote": "<span id=\"node-a-e8ee6b4976cd03cc03da5dd5\" class=\"block-anchor\"></span>由于$\\alpha \\wedge *\\beta$是一个$m$次形式，它在$M$上的积分是良定义的。两个$r$次形式的<a class=\"concept-reference\" href=\"01-section-7-1.md#bound-definition-9094fd4d3ca4a94fdb8d5149\"><u class=\"concept-term\" id=\"bound-mention-ab3b87c790db55bcdf26b9c6\" data-concept-identity=\"urn:uuid:0a507b65-dfea-4bc8-ada8-442de630a818\" data-concept-role=\"discussion\" data-concept-first-mention=\"false\" data-concept-navigation-schema=\"1\" data-concept-source-node=\"a-e8ee6b4976cd03cc03da5dd5\" data-concept-identity-status=\"formal\" data-concept-definition-status=\"mention\" data-concept-route=\"/concepts/by-id/0a507b65-dfea-4bc8-ada8-442de630a818\" title=\"查看本书定义\" data-concept-reference=\"bound-definition-9094fd4d3ca4a94fdb8d5149\" data-concept-reference-basis=\"definition\" data-concept-first-mention-target=\"/books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-01/02-section-1-2#bound-first-532258cd337fb2797da2dd95\">内积</u></a>$(\\omega, \\eta)$定义为",
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        "quote": "<span id=\"node-a-a1ba544aa95d5c34c453f426\" class=\"block-anchor\"></span>还可以逐点定义<span class=\"concept-mention-pending\" id=\"bound-first-04f9ddab623a20c2af21a1b8\" data-concept-identity=\"urn:uuid:e2bd0dbc-dc7e-5082-8f9b-f42efeedebda\" data-concept-role=\"first-mention\" data-concept-first-mention=\"true\" data-concept-navigation-schema=\"1\" data-concept-source-node=\"a-a1ba544aa95d5c34c453f426\" data-concept-identity-status=\"provisional\" data-concept-definition-status=\"candidate\">纤维度量(fibre metric)</span> $h_{\\mu \\nu}(p)$。设 $s$ 与 $s'$ 是 $U_i$ 上的截面，则 $s$ 与 $s'$ 在 $p$ 处的<a class=\"concept-reference\" href=\"../chapter-07/01-section-7-1.md#bound-definition-9094fd4d3ca4a94fdb8d5149\"><u class=\"concept-term\" id=\"bound-mention-b8c8724f6edbb14a5de9106e\" data-concept-identity=\"urn:uuid:0a507b65-dfea-4bc8-ada8-442de630a818\" data-concept-role=\"discussion\" data-concept-first-mention=\"false\" data-concept-navigation-schema=\"1\" data-concept-source-node=\"a-a1ba544aa95d5c34c453f426\" data-concept-identity-status=\"formal\" data-concept-definition-status=\"mention\" data-concept-route=\"/concepts/by-id/0a507b65-dfea-4bc8-ada8-442de630a818\" title=\"查看本书定义\" data-concept-reference=\"bound-definition-9094fd4d3ca4a94fdb8d5149\" data-concept-reference-basis=\"definition\" data-concept-first-mention-target=\"/books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-01/02-section-1-2#bound-first-532258cd337fb2797da2dd95\">内积</u></a>定义为",
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