Remember that the curvature depends only on the coefficients of the first fundamental form. There exists a very tedious formula for this.
Show that if the first fundamental form with respect to the given parametrization x(u,v) of a surface has the form
du^{2}+2cosw(u,v)dudv+dv^{2} for some function w, then the gaussian curvature K=-w_{uv}/sinw.
Attempt:
E=1
F=cosw(u,v)
G=1
K=eg-f^{2}/EG-F^{2 }I don't know how to find the 2nd fundamental form coefficients with the given information. Or is there another way to solve?
Remember that the curvature depends only on the coefficients of the first fundamental form. There exists a very tedious formula for this.