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

Tongzhu Li

doi:10.1007/s11401-017-1028-2

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

Tongzhu Li^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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
Pages (from-to)	1131-1144
Number of pages	14
Journal	Chinese Annals of Mathematics. Series B
Volume	38
Issue number	5
DOIs	https://doi.org/10.1007/s11401-017-1028-2
Publication status	Published - 1 Sept 2017

Keywords

Conformal transformation group
Möbius homogeneous hypersurfaces
Möbius isoparametric hypersurfaces
Möbius transformation group

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10.1007/s11401-017-1028-2

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title = "M{\"o}bius homogeneous hypersurfaces with three distinct principal curvatures in Sn+1 ",

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 M{\"o}bius 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 M{\"o}bius homogeneous hypersurface. In this paper, the M{\"o}bius homogeneous hypersurfaces with three distinct principal curvatures are classified completely up to a M{\"o}bius transformation.",

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N2 - 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.

AB - 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.

KW - Conformal transformation group

KW - Möbius homogeneous hypersurfaces

KW - Möbius isoparametric hypersurfaces

KW - Möbius transformation group

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JF - Chinese Annals of Mathematics. Series B

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ER -

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

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