Let (M~,〈,〉) be a Riemannian manifold, and (M,g) be a Riemannian submanifold of M~. We want to compute the curvature of M in terms of the curvature of M~. We first consider the case where M is an hypersurface of M~ (the reader can keep in mind the example of surfaces in R3). The general case is treated in exercise.
KeywordsVector Field Riemannian Manifold Orthonormal Basis Sectional Curvature Fundamental Form
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