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Classification of the Blaschke Isoparametric Hypersurfaces with Three Distinct Blaschke Eigenvalues

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Abstract

An immersed umbilic-free submanifold in the unit sphere is called Blaschke isoparametric if its Möbius form vanishes identically and all of its Blaschke eigenvalues are constant. Then the classification of Blaschke isoparametric hypersurfaces is natural and interesting in the Möbius geometry of submanifolds. In this paper, we give a classification of the Blaschke isoparametric hypersurfaces with three distinct Blaschke eigenvalues one of which is simple.

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Authors and Affiliations

  1. Department of Mathematics, Henan Normal University, Jian She Dong Lu 46, Xin Xiang, 453007, Henan, People’s Republic of China

    Xingxiao Li & Yejuan Peng

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  1. Xingxiao Li
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  2. Yejuan Peng
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Correspondence to Xingxiao Li.

Additional information

Research partially supported by NNSF of China (10671181), NSF of Henan Province Science and Technology Department (092300410143), and NSF of Henan Province education Department (2009A110010).

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Li, X., Peng, Y. Classification of the Blaschke Isoparametric Hypersurfaces with Three Distinct Blaschke Eigenvalues. Results. Math. 58, 145–172 (2010). https://doi.org/10.1007/s00025-010-0033-5

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  • DOI: https://doi.org/10.1007/s00025-010-0033-5

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