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

“E=⃑x_u·⃑x_u”

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Meanings

nounfirst fundamental form (uncountable)
  1. uncountabledifferential geometrythe 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

    2 more examples

    F=⃑x_u·⃑x_v

    G=⃑x_v·⃑x_v

Cite this entry
APA

first fundamental form. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/first%20fundamental%20form

MLA

“first fundamental form.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/first%20fundamental%20form. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “first fundamental form,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/first%20fundamental%20form.

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