science forum addict
Joined: 06 May 2005
|Posted: Fri Jul 21, 2006 7:52 am Post subject:
Considering a one-parameter group f: M x R -> M, where M is a
differentiable manifold; is it true that its infinitesimal generator,
namely the vector vield which associates to x the tangent vector at
point x given by the curve t->f(x,t), is a C^(+oo) vector field ?
I read that thing in Sternberg's course (5.3 p.380, Advanced Calculus),
but it seems to me that since f is supposed to be only differentiable,
the infinitesimal generator of f should be only differentiable ...
Maybe there is some inductive stuff that guarantees C^(+oo), but I
can't see it ...
Thanks for any help,