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        "quote": "对每个 1-形式 $\\omega$ 和向量场 $X$。$DY$ 的张量性质由对两个自变量的线性性推出。对 $\\omega$ 的线性性是平凡的，而对 $X$ 的线性性则直接由 (Con1) 和 (Con2) 推出。张量场 $DY$ 称为向量场 $Y$ 的 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:97514113-7cb5-48b4-9541-733ea93565c0\" data-concept-route=\"/concept-identities#concept-97514113-7cb5-48b4-9541-733ea93565c0\" id=\"first-34eace036055d44a85b5-zh\">协变导数(covariant derivative)</u>。这里所描述的联络理论称为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:0b12bccf-e600-4e8b-8f23-c741396d237f\" data-concept-route=\"/concept-identities#concept-0b12bccf-e600-4e8b-8f23-c741396d237f\" id=\"first-77aefb7fa1e7bce3b19b-zh\">科苏尔联络(Koszul connection)</u> [1–6]，而将在下文推导出的“老式”坐标版本则见于 [7, 8] 等文献。",
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        "quote": "for every 1-form $\\omega$ and vector field $X$. The tensor nature of $DY$ follows from linearity in both arguments. Linearity in $\\omega$ is trivial, while linearity in $X$ follows immediately from (Con1) and (Con2). The tensor field $DY$ is called the <u class=\"concept-term\" data-concept-identity=\"urn:uuid:97514113-7cb5-48b4-9541-733ea93565c0\" data-concept-route=\"/concept-identities#concept-97514113-7cb5-48b4-9541-733ea93565c0\" id=\"first-34eace036055d44a85b5-en\">covariant derivative</u> of the vector field $Y$. The theory of connections as described here is called a <u class=\"concept-term\" data-concept-identity=\"urn:uuid:0b12bccf-e600-4e8b-8f23-c741396d237f\" data-concept-route=\"/concept-identities#concept-0b12bccf-e600-4e8b-8f23-c741396d237f\" id=\"first-77aefb7fa1e7bce3b19b-en\">Koszul connection</u> [1–6], while the ‘old-fashioned’ coordinate version that will be deduced below appears in texts such as [7, 8].",
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