In this chapter, we study the relations between the Riemannian Geometry of a submanifold and that of the ambient 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.
KeywordsRiemannian Manifold Minimal Surface Sectional Curvature Fundamental Form Gaussian Curvature
Unable to display preview. Download preview PDF.