first fundamental form en · NOUN
Meanings
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(qualifier:differential geometry, uncountable) the Riemannian metric for 2-dimensional manifolds, i.e. given a surface with regular parametrization x(u,v), the first fundamental form is a set of three functions, {E, F, G}, dependent on u and v, which give information about local intrinsic curvature of the surface. These functions are given by
F=⃑x_u·⃑x_v
E=⃑x_u·⃑x_u
G=⃑x_v·⃑x_v