Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length

  • S. S. Chern
  • M. do Carmo
  • S. Kobayashi
Chapter

Abstract

Let \(\text M\)be an n-dimensional manifold which is minimally immersed in a unit sphere \(S^{n+p}\)of dimension \(n+p.\)

Keywords

Scalar Curvature Fundamental Form Constant Curvature Isometric Immersion Connection Form 
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References

  1. 1.
    Boruvka, o.: Sur les surfaces representées par les fonctions sphériques de première espèce. J. Math. pure et appl. 12, 337—383 (1933).Google Scholar
  2. 2.
    Lawson, B.: Local rigidity theorems for minimal hypersurfaces. Ann. of Math. 89, 187—197 (1969).MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Simons, J.: Minimal varieties in riemannian manifolds. Ann. of Math. 88, 62—105 (1968).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • S. S. Chern
    • 1
    • 2
  • M. do Carmo
    • 1
    • 2
  • S. Kobayashi
    • 1
    • 2
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.IMPARio de JaneiroBrasil

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