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Differential Manifolds

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

Abstract

A subset MRn+k is an n-dimensional submanifold of class Cp of Rn+k if, for any χ ∈ M, there exists a neighborhood U of χ in Rn+k and a C p submersion f: UR k such that UM = f−1 (0) (we recall tnat f is a submersion if its differential map is surjective at each point).

Keywords

Vector Field Vector Bundle Open Subset Volume Form Smooth Manifold 
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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