Möbius Homogeneous Hypersurfaces with One Simple Principal Curvature in Sn+1

Ya Yun Chen; Xiu Ji; Tong Zhu Li

doi:10.1007/s10114-020-9431-0

Möbius Homogeneous Hypersurfaces with One Simple Principal Curvature in Sⁿ⁺¹

Ya Yun Chen, Xiu Ji, Tong Zhu Li^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

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

1 Citation (Scopus)

Abstract

Let Möb(Sⁿ⁺¹) denote the Möbius transformation group of Sⁿ⁺¹. A hypersurface f: Mⁿ → Sⁿ⁺¹ is called a Möbius homogeneous hypersurface, if there exists a subgroup G (Formula presented.)Möb(Sⁿ⁺¹) such that the orbit G(p) = {ϕ(p) ∣ ϕ ∈ G} = f (Mⁿ),p ∈ f (Mⁿ). In this paper, we classify the Möbius homogeneous hypersurfaces in Sⁿ⁺¹ with at most one simple principal curvature up to a Möbius transformation.

Original language	English
Pages (from-to)	1001-1013
Number of pages	13
Journal	Acta Mathematica Sinica, English Series
Volume	36
Issue number	9
DOIs	https://doi.org/10.1007/s10114-020-9431-0
Publication status	Published - 1 Sept 2020

Keywords

51B10
53C30
Möbius homogeneous hypersurfaces
Möbius transformation group
homogeneous hypersurfaces
isometric transformation group

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10.1007/s10114-020-9431-0

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abstract = "Let M{\"o}b(Sn+1) denote the M{\"o}bius transformation group of Sn+1. A hypersurface f: Mn → Sn+1 is called a M{\"o}bius homogeneous hypersurface, if there exists a subgroup G (Formula presented.)M{\"o}b(Sn+1) such that the orbit G(p) = {ϕ(p) ∣ ϕ ∈ G} = f (Mn),p ∈ f (Mn). In this paper, we classify the M{\"o}bius homogeneous hypersurfaces in Sn+1 with at most one simple principal curvature up to a M{\"o}bius transformation.",

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doi = "10.1007/s10114-020-9431-0",

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AU - Chen, Ya Yun

AU - Ji, Xiu

AU - Li, Tong Zhu

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Y1 - 2020/9/1

N2 - Let Möb(Sn+1) denote the Möbius transformation group of Sn+1. A hypersurface f: Mn → Sn+1 is called a Möbius homogeneous hypersurface, if there exists a subgroup G (Formula presented.)Möb(Sn+1) such that the orbit G(p) = {ϕ(p) ∣ ϕ ∈ G} = f (Mn),p ∈ f (Mn). In this paper, we classify the Möbius homogeneous hypersurfaces in Sn+1 with at most one simple principal curvature up to a Möbius transformation.

AB - Let Möb(Sn+1) denote the Möbius transformation group of Sn+1. A hypersurface f: Mn → Sn+1 is called a Möbius homogeneous hypersurface, if there exists a subgroup G (Formula presented.)Möb(Sn+1) such that the orbit G(p) = {ϕ(p) ∣ ϕ ∈ G} = f (Mn),p ∈ f (Mn). In this paper, we classify the Möbius homogeneous hypersurfaces in Sn+1 with at most one simple principal curvature up to a Möbius transformation.

KW - 51B10

KW - 53C30

KW - Möbius homogeneous hypersurfaces

KW - Möbius transformation group

KW - homogeneous hypersurfaces

KW - isometric transformation group

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Möbius Homogeneous Hypersurfaces with One Simple Principal Curvature in Sⁿ⁺¹

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Keywords

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