Writing a story about a college math student

[Jared1]

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.

 

[Jared1]

Does anyone have any suggestions for this?

 

[Jared1]

Hello?

 

[zhentil]

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.

 

[Jared1]

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