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.
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Cecil, T. E. and Ryan, P. J.: Tight and Taut Immersions of Manifolds, Pitman Advanced Publishing Program, 1985.
Cheng, S. Y. and Yau, S. T.: Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), 195–204.
Derdziński, A. and Shen, C. L.: Codazzi tensor fields, curvature and Pontryagin forms, Proc. London Math. Soc., 47(3) (1983), 15–26.
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.
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.
Nomizu, K.: On isoparametric hypersurfaces in the Lorentzian space forms, Japan J. Math. 7 (1981), 217–226.
Simon, U.: Codazzi Tensors, Lecture Notes in Mathematics, Vol. 838 (1979), pp. 289–296.
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Haizhong, L. Generalized Cartan Identities on Isoparametric Manifolds. Annals of Global Analysis and Geometry 15, 45–50 (1997). https://doi.org/10.1023/A:1006528906547
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DOI: https://doi.org/10.1023/A:1006528906547