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first fundamental form

noun

Definitions

  1. the Riemannian metric for 2-dimensional manifolds, i.e. given a surface with regular…

    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

    • E=⃑x_u·⃑x_u
    • F=⃑x_u·⃑x_v
    • G=⃑x_v·⃑x_v

The neighborhood

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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA