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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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.
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
- Möbius transformation group
- Conformal transformation group
- Möbius homogeneous hypersurfaces
- Möbius isoparametric hypersurfaces
2000 MR Subject Classification