切丛

阐述

设 $M^n$ 是一个微分流形，则它的切丛

T M=\left\{(p, v) ; p \in M, v \in T_{p} M\right\}

也是一个微分流形，而对应于原有的每个参数化 $U_\alpha,x_\alpha$ 来说，都有

\begin{array}{c}\mathbf{y}_{\alpha}\left(x_{1}^{\alpha}, \ldots, x_{n}^{\alpha}, u_{1}, \ldots, u_{n}\right)= \\ =\left(\mathbf{x}_{\alpha}\left(x_{1}^{\alpha}, \ldots, x_{n}^{\alpha}\right), \sum_{i=1}^{n} u_{i} \frac{\partial}{\partial x_{i}^{\alpha}}\right), \quad\left(u_{1}, \ldots, u_{n}\right) \in \mathbf{R}^{n}\end{array}