Riemannian submanifolds

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


In this chapter, we study the relations between the Riemannian Geometry of a submanifold and that of the ambient 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.


Riemannian Manifold Minimal Surface Sectional Curvature Fundamental Form Gaussian Curvature 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Sylvestre Gallot
    • 1
  • Dominique Hulin
    • 2
  • Jacques Lafontaine
    • 3
  1. 1.Institut Fourier, C.N.R.S., UMR 5582Université Grenoble 1Saint-Martin d’HèresFrance
  2. 2.Département de MathématiquesUniversité Paris XIOrsay CXFrance
  3. 3.Département de Mathématiques, C.N.R.S., UMR 5149Université Montpellier IIMontpellier CX 05France

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