first fundamental form

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English

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first fundamental form

Noun

first fundamental form (uncountable)

(differential geometry) 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
$E={\vec {x}}_{u}\cdot {\vec {x}}_{u}$

$F={\vec {x}}_{u}\cdot {\vec {x}}_{v}$

$G={\vec {x}}_{v}\cdot {\vec {x}}_{v}$

Translations

metric

Bulgarian: ^{(please verify)} първа квадратична форма (pǎrva kvadratična forma)

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