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Riemannian Metrics

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

Abstract

A Riemannian metric on a manifold M is a family of scalar products defined on each tangent space TmM and depending smoothly on m:

2.1 Definition : A Riemannian metric on M is a smooth and positive definite section g of the bundle S2T*M of the symmetric bilinear 2-forms on M.

Keywords

Vector Field Riemannian Manifold Homogeneous Space Parallel Transport Klein Bottle 
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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