Let x : U subset of R2 -> X be a parametrization of the surface X. Show that the first fundamental form of X is positive definite if and only if the parametrization is regular
(i.e., at every point the coordinate vectors x1 and x2 span a plane)
Let x : U subset of R2 -> X be a parametrization of the surface X. Show that the first fundamental form of X is positive definite if and only if the parametrization is regular
(i.e., at every point the coordinate vectors x1 and x2 span a plane)