I must demonstrate in two ways that if c(t) is an integral curve of a smooth vector field X on a smooth manifold M with c'(t_0)=0 for some t_0, then c is a constant curve.(adsbygoogle = window.adsbygoogle || []).push({});

I found one way: If [itex]\theta[/itex] denotes the flow of X, then because X is invariant under its own flow, we have

[tex]c'(t)=X_{c(t)} = (\theta_{t-t_0})_*X_{c(t_0)}=(\theta_{t-t_0})_*c'(t_0)=0[/tex]

for all t.

Does anyone see another way?

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# A problem about integral curves on a manifold

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