first fundamental form

noun

first fundamental form

noun

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

Differential geometry

E=⃑x_u·⃑x_u
F=⃑x_u·⃑x_v

1 more example

G=⃑x_v·⃑x_v

Entry derived from the Wiktionary, under licence CC BY-SA 4.0 — list of authors.