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| ``Re: inclusion map on Riemannian manifolds''
by ulrich_utiger on 2006-04-14 07:25:44 |
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| That's an interesting theorem. Maybe my prof was thinking to that. By the why you made an error in your notation: if F = hfg^(-1) then
F : g(G) \subset IR^m --> h(H) \subset IR^n.
It is also possible that my prof was confusing the two definitions of a submanifold:
1. If the inclusion i:M->N is an embedding then M is a submanifold.
2. A subset M of a manifold N with dimension n is a submanifold of dimension m if there is a chart h:N->Rn with a coordinate neighbourhood H in N such that
h(H intersection M) = {x of h(H) | x(m+1)=x(m+2)=...xn=0}.
I think my prof is confusing i and h, which are not the same. I guess to prove the equivalence of these two definitions is a bit more complicate than just to equal i and h. I am wondering how this can be done. Any suggestions?
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