Definitions for first fundamental form

This page provides all possible meanings and translations of the word first fundamental form


  1. 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


  1. 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.

Images & Illustrations of first fundamental form


Find a translation for the first fundamental form definition in other languages:

Select another language:

Discuss these first fundamental form definitions with the community:

Word of the Day

Would you like us to send you a FREE new word definition delivered to your inbox daily?

Please enter your email address:     


Use the citation below to add this definition to your bibliography:


"first fundamental form." STANDS4 LLC, 2015. Web. 1 Dec. 2015. < fundamental form>.

Are we missing a good definition for first fundamental form? Don't keep it to yourself...

Nearby & related entries:

Alternative searches for first fundamental form:

Thanks for your vote! We truly appreciate your support.