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        "quote": "由于 $p$ 是 $M$ 的任意点，我们得到 $M ,$ 上的一个向量场 $X$，称为由流 $\\sigma$ 诱导的向量场。任何由 $M$ 的单参数变换群诱导的向量场 $X$ 都称为 <u id=\"concept-15-complete-vector-field\" class=\"concept-term\" data-concept-identity=\"urn:uuid:042328bd-d5e2-4fe7-8a36-2a21890d5e6f\" data-concept-route=\"/concept-identities#concept-042328bd-d5e2-4fe7-8a36-2a21890d5e6f\">完备向量场(complete vector field)</u>。单参数群 $\\sigma _ { t }$ 可以看作是用一族曲线“填充”向量场 $X$，这些曲线扮演着流体流线的角色，而该流体的速度处处由 $X$ 给出（见图 15.6）。",
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        "quote": "Since $p$ is an arbitrary point of $M$ we have a vector field $X$ on $M ,$ said to be the vector field induced by the flow $\\sigma$. Any vector field $X$ induced by a one-parameter group of transformations of $M$ is said to be <u class=\"concept-term\" data-concept-identity=\"urn:uuid:042328bd-d5e2-4fe7-8a36-2a21890d5e6f\" data-concept-route=\"/concept-identities#concept-042328bd-d5e2-4fe7-8a36-2a21890d5e6f\" id=\"first-d4248df8d36a72045755-vector-field-en\">complete</u>. The one-parameter group $\\sigma _ { t }$ can be though of as ‘filling in’ the vector field $X$ with a set of curves, which play the role of streamlines for a fluid whose velocity is everywhere given by $X$ (see Fig. 15.6).",
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