Functions on manifolds

  • #1

Main Question or Discussion Point

Assume you have two manifolds M and N diffeomorphic to another. Also, there is a real-valued function f defined on M.

What happens with f when you go from M to N? How is f related to N?

thanks
 

Answers and Replies

  • #2
108
1
If you have a map from M to N does the map not also act on the function f and transform it appropriately?
 
  • #3
What actually does diffeomorphic really mean?

Take a manifold M without Riemann structure defined on, i.e. without any geometric properties, so that makes it very malleable.

Is not every manifold diffeomorphic to M already M?
 
  • #4
If my manifold M can be a ball, a cigar or what have you, what then is a to M diffeomorphic manifold N?
 
  • #5
389
0
What happens with f when you go from M to N? How is f related to N?
Consider the diffeomorphism g:M-->N.
Then you have that the composition of g^-1 and f, maps from N to R. Is that what you are looking for?
 

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