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        "quote": "有时被称为 $\\alpha$ 的 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:e372d315-1f44-4cdf-9f85-d01e74317539\" data-concept-route=\"/concept-identities#concept-e372d315-1f44-4cdf-9f85-d01e74317539\" id=\"first-2671483f7260b6048199-zh\">周期(period)</u>。由斯托克斯定理，若 $\\alpha$ 是恰当形式，则 $\\alpha$ 的所有周期都为零，而任何闭的 $r$-形式在边界 $r$-循环 $C = \\partial C ^ { \\prime }$ 上的周期为零。设 $C _ { 1 } , \\ldots , C _ { k }$ 是 $Z _ { r } ( M )$ 中 $k = b _ { r }$ 个线性无关的循环，使得当 $i \\neq j$ 时 $[ C _ { i } ] \\neq [ C _ { j } ]$。德拉姆定理蕴含，一个 $r$-形式 $\\alpha$ 是恰当的，当且仅当所有周期 $\\textstyle \\int _ { C _ { i } } \\alpha = 0$。若 $\\alpha$ 是恰当的，则我们已经指出它的所有周期都为零。逆命题由以下事实推出：对每个 $[ C ] \\in H _ { r } ( M )$ 都有 $\\langle [ C ] , [ \\alpha ] \\rangle = 0$，因为 [$C$] 可以展开为 $\\textstyle [ C ] = \\sum _ { i = 1 } ^ { k } [ C _ { i } ]$。由乘积的非退化性，我们必须有 $[ \\alpha ] = 0$，从而对某个 $(r-1)$-形式 $\\beta .$ 有 $\\alpha = \\mathrm { d } \\beta$。",
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