In this chapter, we study the relations between the Riemannian Geometry of a submanifold and that of the ambiant space. It is well known that surfaces of the Euclidean space were the first examples of Riemannian manifolds to be studied. In fact, the first truly Riemannian geometry result is due to Gauss, and roughly says the following.
KeywordsSectional Curvature Fundamental Form Gaussian Curvature Principal Curvature Isometric Immersion
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