# Thread: Given first fundamental form, find gaussian curvature

1. ## Given first fundamental form, find gaussian curvature

Show that if the first fundamental form with respect to the given parametrization x(u,v) of a surface has the form
du2+2cosw(u,v)dudv+dv2 for some function w, then the gaussian curvature K=-wuv/sinw.

Attempt:
E=1
F=cosw(u,v)
G=1

K=eg-f2/EG-F2

I don't know how to find the 2nd fundamental form coefficients with the given information. Or is there another way to solve?

2. ## Re: Given first fundamental form, find gaussian curvature

Remember that the curvature depends only on the coefficients of the first fundamental form. There exists a very tedious formula for this.