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Riemannian Submanifolds

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

Abstract

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.

Keywords

Vector Field Riemannian Manifold Orthonormal Basis Sectional Curvature Fundamental Form 
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 1987

Authors and Affiliations

  • Sylvestre Gallot
    • 1
  • Dominique Hulin
    • 2
  • Jacques Lafontaine
    • 3
  1. 1.Université de SavoieChambéry CedexFrance
  2. 2.Centre d’Orsay, MathématiqueUniversité Paris11Orsay CedexFrance
  3. 3.U.F.R. de MathématiquesUniversité Paris 7Paris Cedex 05France

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