Möbius homogeneous hypersurfaces in Sn+1

Tongzhu Li; Xiang Ma; Changping Wang; Peng Wang

doi:10.1016/j.aim.2024.109722

Möbius homogeneous hypersurfaces in Sⁿ⁺¹

Tongzhu Li^*, Xiang Ma, Changping Wang, Peng Wang

^*Corresponding author for this work

School of Mathematics and Statistics

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

Abstract

Let M(Sⁿ⁺¹) denote the Möbius transformation group of the (n+1)-dimensional sphere Sⁿ⁺¹. A hypersurface x:Mⁿ→Sⁿ⁺¹ is called a Möbius homogeneous hypersurface if there exists a subgroup G of M(Sⁿ⁺¹) such that the orbit G⋅p=x(Mⁿ),p∈x(Mⁿ). In this paper, the Möbius homogeneous hypersurfaces are classified completely up to a Möbius transformation of Sⁿ⁺¹.

Original language	English
Article number	109722
Journal	Advances in Mathematics
Volume	448
DOIs	https://doi.org/10.1016/j.aim.2024.109722
Publication status	Published - Jun 2024

Keywords

Möbius form
Möbius homogeneous hypersurface
Möbius principal curvature
Möbius transformation group

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10.1016/j.aim.2024.109722

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title = "M{\"o}bius homogeneous hypersurfaces in Sn+1",

abstract = "Let M(Sn+1) denote the M{\"o}bius transformation group of the (n+1)-dimensional sphere Sn+1. A hypersurface x:Mn→Sn+1 is called a M{\"o}bius homogeneous hypersurface if there exists a subgroup G of M(Sn+1) such that the orbit G⋅p=x(Mn),p∈x(Mn). In this paper, the M{\"o}bius homogeneous hypersurfaces are classified completely up to a M{\"o}bius transformation of Sn+1.",

keywords = "M{\"o}bius form, M{\"o}bius homogeneous hypersurface, M{\"o}bius principal curvature, M{\"o}bius transformation group",

author = "Tongzhu Li and Xiang Ma and Changping Wang and Peng Wang",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Inc.",

year = "2024",

month = jun,

doi = "10.1016/j.aim.2024.109722",

language = "English",

volume = "448",

journal = "Advances in Mathematics",

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T1 - Möbius homogeneous hypersurfaces in Sn+1

AU - Li, Tongzhu

AU - Ma, Xiang

AU - Wang, Changping

AU - Wang, Peng

PY - 2024/6

Y1 - 2024/6

N2 - Let M(Sn+1) denote the Möbius transformation group of the (n+1)-dimensional sphere Sn+1. A hypersurface x:Mn→Sn+1 is called a Möbius homogeneous hypersurface if there exists a subgroup G of M(Sn+1) such that the orbit G⋅p=x(Mn),p∈x(Mn). In this paper, the Möbius homogeneous hypersurfaces are classified completely up to a Möbius transformation of Sn+1.

AB - Let M(Sn+1) denote the Möbius transformation group of the (n+1)-dimensional sphere Sn+1. A hypersurface x:Mn→Sn+1 is called a Möbius homogeneous hypersurface if there exists a subgroup G of M(Sn+1) such that the orbit G⋅p=x(Mn),p∈x(Mn). In this paper, the Möbius homogeneous hypersurfaces are classified completely up to a Möbius transformation of Sn+1.

KW - Möbius form

KW - Möbius homogeneous hypersurface

KW - Möbius principal curvature

KW - Möbius transformation group

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U2 - 10.1016/j.aim.2024.109722

DO - 10.1016/j.aim.2024.109722

M3 - Article

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SN - 0001-8708

VL - 448

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 109722

ER -

Möbius homogeneous hypersurfaces in Sⁿ⁺¹

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Keywords

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