Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Functions on manifolds

  1. Apr 30, 2008 #1
    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?

  2. jcsd
  3. May 1, 2008 #2
    If you have a map from M to N does the map not also act on the function f and transform it appropriately?
  4. May 5, 2008 #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?
  5. May 6, 2008 #4
    If my manifold M can be a ball, a cigar or what have you, what then is a to M diffeomorphic manifold N?
  6. May 6, 2008 #5
    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook