According to Isham (Differential Geometry for Physics) at page 115 he claims:(adsbygoogle = window.adsbygoogle || []).push({});

"If X is a complete vector field then V can always be chosen to be the entire manifold M"

where V is an open subset of a manifold M. He leaves this claim unproved.

A complete vector field is a vector field which has integral curves defined on the whole of ##\mathbb{R}##. Does the claim somehow follow from the definition?

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# Complete vector field X => X defined on the whole manifold?

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