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^*

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

5 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	1131-1144
页数	14
期刊	Chinese Annals of Mathematics. Series B
卷	38
期	5
DOI	https://doi.org/10.1007/s11401-017-1028-2
出版状态	已出版 - 1 9月 2017

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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.",

keywords = "Conformal transformation group, M{\"o}bius homogeneous hypersurfaces, M{\"o}bius isoparametric hypersurfaces, M{\"o}bius transformation group",

author = "Tongzhu Li",

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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.

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JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

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

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