first fundamental form

Hello, you have come here looking for the meaning of the word first fundamental form. In DICTIOUS you will not only get to know all the dictionary meanings for the word first fundamental form, but we will also tell you about its etymology, its characteristics and you will know how to say first fundamental form in singular and plural. Everything you need to know about the word first fundamental form you have here. The definition of the word first fundamental form will help you to be more precise and correct when speaking or writing your texts. Knowing the definition offirst fundamental form, as well as those of other words, enriches your vocabulary and provides you with more and better linguistic resources.

English

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
$E={\vec {x}}_{u}\cdot {\vec {x}}_{u}$

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

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

Wikious

Boobota

Sagapedia