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Writing a story about a college math student

  1. Jan 14, 2009 #1
    Hello, everyone:

    I have a bit of a strange question, but I am a writer and I'm writing a story about a college math student. What I'm in need of is an example of a question in Differential Geometry involving a "Submersion" (preferably a word problem), the process, and the solution.

    The math question will come to parallel the events in the main character's life.

    If anyone can give me an example of a question, process, and solution, it would be warmly appreciated. Please feel free to post on here, or e-mail me at jared.shipley@hotmail.com.

    Thanks, everyone!
    Jared S.
     
  2. jcsd
  3. Jan 16, 2009 #2
    Re: Submersion

    Does anyone have any suggestions for this?
     
  4. Jan 19, 2009 #3
    Re: Submersion

    Hello?
     
  5. Jan 20, 2009 #4
    Re: Submersion

    Let (M,g) be a Riemannian manifold, N be a manifold, and p:M->N a surjective submersion. Suppose also that there exists a lie group G acting transitively on the fibers of p, with p(g*x) = p(x) for all g in G, x in M. Show that there exists a unique metric h on N such that p is a Riemannian submersion.
     
  6. Jan 20, 2009 #5
    Re: Submersion

    This will be great! Thank you so much! I appreciate it!
     
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