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Annals of Global Analysis and Geometry

, Volume 15, Issue 1, pp 45–50 | Cite as

Generalized Cartan Identities on Isoparametric Manifolds

  • Li Haizhong
Article

Abstract

We first introduce the concept of an isoparametric manifold, which is the natural generalization of the concept of an isoparametric hypersurface in a real space form and that of a space-like isoparametric hypersurface in a Lorentzian space form. Finally, we establish generalized Cartan identities for isoparametric manifolds.

isoparametric hypersurface Codazzi tensor 

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References

  1. 1.
    Cecil, T. E. and Ryan, P. J.: Tight and Taut Immersions of Manifolds, Pitman Advanced Publishing Program, 1985.Google Scholar
  2. 2.
    Cheng, S. Y. and Yau, S. T.: Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), 195–204.zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Derdziński, A. and Shen, C. L.: Codazzi tensor fields, curvature and Pontryagin forms, Proc. London Math. Soc., 47(3) (1983), 15–26.MathSciNetGoogle Scholar
  4. 4.
    Oliker, V. I. and Simon, U.: Codazzi tensors and equations of Monge-Ampere type on compact manifolds of constant sectional curvature, J. Reine Angew. Math. 342 (1983), 35–65.zbMATHMathSciNetGoogle Scholar
  5. 5.
    Nomizu, K.: Elie Cartan's work on isoparametric families of hypersurfaces, Proc. Symposia in Pure Math., Amer. Math. Soc. 27(part 2), (1975), 191–200.zbMATHMathSciNetGoogle Scholar
  6. 6.
    Nomizu, K.: On isoparametric hypersurfaces in the Lorentzian space forms, Japan J. Math. 7 (1981), 217–226.zbMATHMathSciNetGoogle Scholar
  7. 7.
    Simon, U.: Codazzi Tensors, Lecture Notes in Mathematics, Vol. 838 (1979), pp. 289–296.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Li Haizhong
    • 1
  1. 1.Department of Applied MathematicsTsinghua UniversityBeijingPeople's Republic of China

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