Abstract
Let x: Mn → Sn+1 be an immersed hypersurface in the (n + 1)-dimensional sphere Sn+1. If, for any points p, q ∈ Mn, there exists a Möbius transformation ϕ: Sn+1 → Sn+1 such that ϕ ○ x(Mn) = x(Mn) 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.
Original language | English |
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Pages (from-to) | 1131-1144 |
Number of pages | 14 |
Journal | Chinese Annals of Mathematics. Series B |
Volume | 38 |
Issue number | 5 |
DOIs | |
Publication status | Published - 1 Sept 2017 |
Keywords
- Conformal transformation group
- Möbius homogeneous hypersurfaces
- Möbius isoparametric hypersurfaces
- Möbius transformation group
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Li, T. (2017). Möbius homogeneous hypersurfaces with three distinct principal curvatures in Sn+1 Chinese Annals of Mathematics. Series B, 38(5), 1131-1144. https://doi.org/10.1007/s11401-017-1028-2