Let Support (X) is compact , then X is a complete vector filed

239 Views Asked by At

This question is from my assignment on vector fields and I was unable to solve it.

Let M be a smooth manifold and X be a vector field on M. Support (X)={$\overline {p\in M : X_p \neq 0}$}. Prove that if support (X) is compact, then X is a complete vector field.

Attempt: I tried by assuming that there exists a sequence {$x_n$} whose limit (say x)doesn't belongs to X.So, a tangent vector $T_x$ can't be assigned to x. But how do I use the fact that support is not compact?

Kindly give some hints!