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"quote": "流形 $M$ 上类型为 (0, 2) 的张量场 $g$ 称为非奇异的，如果 $g _ { p } \\in T ^ { ( 0 , 2 ) }$ 在每一点 $p \\in M$ 处都是非奇异张量。一个 伪黎曼流形(pseudo-Riemannian manifold) $( M , g )$ 由一个可微流形 $M$ 连同类型为 (0, 2) 的对称非奇异张量场 $g$ 组成，该张量场称为 度量张量(metric tensor)。这等价于在每一点 $p \\in M$ 处的切空间 $T _ { p } ( M )$ 上定义一个内积 $X _ { p } \\cdot Y _ { p } = g _ { p } ( X _ { p } , Y _ { p } )$（见第 5 章和第 7 章）。我们将假设 $g$ 是可微张量场，从而对于每一对光滑向量场 $X$、$Y \\in { \\mathcal { T } } ( M )$，其内积都是可微函数，",
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