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Riemannian Submanifolds

  • Sylvestre Gallot
  • Dominique Hulin
  • Jacques Lafontaine
Part of the Universitext book series (UTX)

Abstract

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.

Keywords

Sectional Curvature Fundamental Form Gaussian Curvature Principal Curvature Isometric Immersion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Sylvestre Gallot
    • 1
  • Dominique Hulin
    • 1
  • Jacques Lafontaine
    • 2
  1. 1.Ecole Polytechnique, Unité de Recherche Associée du CNRS D 0169Centre de MathématiquesPalaiseau CedexFrance
  2. 2.Départment de Mathématiques, GETODIM - Unité de Recherche Associée du CNRS 1407Université de MontpellierMontpellier Cedex 5France

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