Banaras Hindu University

The Second Fundamental Form and the Weingarten Map, Principal, Gaussian and Mean Curvatures. Isometries of surfaces, Gauss's Theorema Egregium, The Fundamental Theorem of Surfaces, Surfaces of Constant Gaussian Curvature. Exponential map, Gauss Lemma, Geodesic Coordinates. The Gauss-Bonnet Formula and the Gauss-Bonnet Theorem (description only). ................
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