P(u,v)=(f(v)cos(u),f(v)sin(v),g(v)) Find formulas for the Christoffel symbols, the second fundamental form, the shape operator, the Gaussian curvature...

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P(u,v)=(f(v)cos(u),f(v)sin(v),g(v))

Find formulas for the Christoffel symbols, the secondfundamental form, the shape operator, the Gaussian curvature andthe mean curvature.

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1 In differential geometry the second fundamentalform or shape tensor is a quadraticform on the tangent plane of a smooth surface in thethreedimensional Euclidean space usually denotedbyread two Together with the first fundamental form it servesto define extrinsic invariants of the surface its principalcurvatures More generally such a quadratic form is defined See Answer

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