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Möbius homogeneous hypersurfaces with three distinct principal curvatures in Sn+1

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Abstract

Let x: M n → Sn+1 be an immersed hypersurface in the (n + 1)-dimensional sphere Sn+1. If, for any points p, q ∈ M n, there exists a Möbius transformation ϕ: Sn+1 → Sn+1 such that ϕ ○ x(M n) = x(M n) and ϕ ○ x(p) = x(q), then the hypersurface is called a Möbius homogeneous hypersurface. In this paper, the Möbius homogeneous hypersurfaces with three distinct principal curvatures are classified completely up to a Möbius transformation.

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Acknowledgments

The author would like to thank Professor Jie Qing for his hospitality and help. The author would also like to thank the referee for some valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, China

    Tongzhu Li

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  1. Tongzhu Li
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Correspondence to Tongzhu Li.

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This work was supported by the National Natural Science Foundation of China (Nos. 11571037, 11471021).

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Li, T. Möbius homogeneous hypersurfaces with three distinct principal curvatures in Sn+1 . Chin. Ann. Math. Ser. B 38, 1131–1144 (2017). https://doi.org/10.1007/s11401-017-1028-2

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  • DOI: https://doi.org/10.1007/s11401-017-1028-2

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