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        "quote": "该证明由令 $T _ { j k } ^ { i } = \\langle { \\mathrm { d } x ^ { i } , \\tau \\left( { \\partial _ { x ^ { j } } , \\partial _ { x ^ { k } } } \\right) } \\rangle$ 并代入<a href=\"#equation-18-19\" class=\"cross-reference\" id=\"xref-03-curvature-and-torsion-4\" data-reference=\"equation-18-19\">式 (18.19)</a> 得出。若一个联络的挠率张量消失，即 $T = 0 ;$ ，则称该联络为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:cb71a150-9540-4253-a1de-4fcb50907875\" data-concept-route=\"/concept-identities#concept-cb71a150-9540-4253-a1de-4fcb50907875\" id=\"first-742245dfca473015595d-zh\">无挠的(torsion-free)</u> 或 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:4cbbafec-2379-4b3d-b21a-4cc767822af7\" data-concept-route=\"/concept-identities#concept-4cbbafec-2379-4b3d-b21a-4cc767822af7\" id=\"first-7014997d70e6559f6fc8-zh\">对称联络(symmetric connection)</u> ；等价地，其分量关于所有坐标对称， $\\Gamma _ { j k } ^ { i } = \\Gamma _ { k j } ^ { i }$",
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        "quote": "The prooffollows from setting $T _ { j k } ^ { i } = \\langle { \\mathrm { d } x ^ { i } , \\tau \\left( { \\partial _ { x ^ { j } } , \\partial _ { x ^ { k } } } \\right) } \\rangle$ and sustituting <a href=\"#equation-18-19\" class=\"cross-reference\" id=\"xref-03-curvature-and-torsion-4\" data-reference=\"equation-18-19\">Eq. (18.19)</a>. We cal a connection <u class=\"concept-term\" data-concept-identity=\"urn:uuid:cb71a150-9540-4253-a1de-4fcb50907875\" data-concept-route=\"/concept-identities#concept-cb71a150-9540-4253-a1de-4fcb50907875\" id=\"first-742245dfca473015595d-en\">torsion-free</u> or <u class=\"concept-term\" data-concept-identity=\"urn:uuid:4cbbafec-2379-4b3d-b21a-4cc767822af7\" data-concept-route=\"/concept-identities#concept-4cbbafec-2379-4b3d-b21a-4cc767822af7\" id=\"first-760eb7e9150caa9c7ef3-connection-en\">symmetric</u> if its torsion tensor vanishes, $T = 0 ;$ ; equivalently, its components are symmetric with respect to all coordinates, $\\Gamma _ { j k } ^ { i } = \\Gamma _ { k j } ^ { i }$",
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