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)

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- May 18th 2010, 06:50 AMtwerdsterFirst Fundamental Form
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)