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center o bass
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According to Isham (Differential Geometry for Physics) at page 115 he claims:
"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?
"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?