# first fundamental form

Definition from Wiktionary, the free dictionary

## English[edit]

### Noun[edit]

**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