Second Fundamental Form
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In differential geometry, the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a differential geometry of surfaces|smooth surface in the three dimensional Euclidean space, usually denoted by \mathrm{I\!I} (read two). Together with the first fundamental form, it serves to define extrinsic invariants of the surface, its principal curvatures. More generally, such a quadratic form is defined for a smooth hypersurface in a Riemannian manifold and a smooth choice of the unit normal vector at each point.
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