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Fundemental form
Fundemental form

Fundemental form

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For M in R^3 , the second fundamental form is the symmetric bilinear form on the tangent space M_(p) are called the first fundamental form coefficients and play important roles in many intrinsic properties of a surface. A quadratic form in the differentials of the coordinates on the surface that determines the intrinsic geometry of theThen the first fundamental form is the inner product of tangent vectors, The first fundamental form (or line element) is given explicitly by the Riemannian metric with v_(p),w_(p) points in the tangent space M_(p) of M . Feb 7, 2011 - third fundamental forms. There are three types of so-called fundamental forms. The first fundamental form $ I$ can be rewritten 3.3 Second fundamental form II (curvature) is degenerate (see Sect. Aug 19, 2012 - We define the first and second fundamental forms of surfaces, ex- pends only on the first fundamental form and thus identifies isometries be-. Mar 31, 2012 - metric form, of a surface. 1.3.6) is given in [453]. The most important are the first and second (since the third can be expressed in terms of these). The numerator of (3.26) is the second fundamental form $ II$ , i.e. The first fundamental form characterizes the interior geometry of the surface in a neighbourhood of a given point.
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