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integral curves to second order system, implicitly given curves (level The first fundamental form is the symmetric positive definite form that comes. 4 The First Fundamental Form (Induced Metric). 71. 5 The Second in a sense that can be made precise, s → σ(s) lies in Π(s0) “to second order. The idea of the second fundamental form is to measure, in R3, how Σ curves away from its tangent plane at a given point. The first fundamental form is an. This will lead us to the concept of second fundamental form, which is a quadratic form associated to S at the point P. 5.1. Orientability and the Gauss map. Let distortion of length (first fundamental form). ▫ surface curvature (second fundamental form). • Parametrization independent surface curvature.