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Definition of First fundamental form
1. Noun. (context: 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 ¹
¹ Source: wiktionary.com