今天的作业,随手写到博客吧. \(Proof.\)对于任意的\(p \in M\),有p附近的坐标卡\((U,x^{1},\ldots,x^{n})\), 由引理\(21.4\),$$dx^{1}\wedge\ldots \wedge dx^{n}(X_{1,p},\ldots,X_{n,p})>0$$ 设\(\beta=dr^{1}\wedge\ldots \wedge dr^{n}\), \[\beta (\frac{\partial }{\partial r^{1} },\ldots,\f