# Definitions for **first fundamental form**

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### Wiktionary

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

### Freebase

First fundamental form

In differential geometry, the first fundamental form is the inner product on the tangent space of a surface in three-dimensional Euclidean space which is induced canonically from the dot product of R. It permits the calculation of curvature and metric properties of a surface such as length and area in a manner consistent with the ambient space. The first fundamental form is denoted by the Roman numeral I, Let X be a parametric surface. Then the inner product of two tangent vectors is where E, F, and G are the coefficients of the first fundamental form. The first fundamental form may be represented as a symmetric matrix.

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"first fundamental form." *Definitions.net.* STANDS4 LLC, 2016. Web. 9 Feb. 2016. <http://www.definitions.net/definition/first fundamental form>.