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

Manifold Covariance Hexagonal Nash Lasso 

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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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