I try to solve this problem:
some smooth path in , and the corresponding surface of revolution.
is a diffeomorphism onto its image.
Find and a function f:U-> ,s.t. 0 is a regular value of f and Im(g)=
I have try to define some function f on a set U, s.t. the Points on the surface are mapped to 0. But i couldn't find it.
My results are quite little, we know that the length of the curve h is 1. Therefore we can find a open set U, which contains the surface.
I try it with some sinus and cosinus relations, like , but it doesn't help. because in equations like f(x,y,z)=x^2+y^2-... we get
How can i define f reasonable?