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

Access to Document

10.1007/s11401-017-1028-2

Cite this

@article{c149ba80464043778a55835402b28b13,

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",

note = "Publisher Copyright: {\textcopyright} 2017, Fudan University and Springer-Verlag GmbH Germany.",

year = "2017",

month = sep,

day = "1",

doi = "10.1007/s11401-017-1028-2",

language = "English",

volume = "38",

pages = "1131--1144",

journal = "Chinese Annals of Mathematics. Series B",

issn = "0252-9599",

publisher = "Springer Verlag",

number = "5",

}

TY - JOUR

T1 - Möbius homogeneous hypersurfaces with three distinct principal curvatures in Sn+1

AU - Li, Tongzhu

PY - 2017/9/1

Y1 - 2017/9/1

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

UR - https://www.scopus.com/pages/publications/85028745931

U2 - 10.1007/s11401-017-1028-2

DO - 10.1007/s11401-017-1028-2

M3 - Article

AN - SCOPUS:85028745931

SN - 0252-9599

VL - 38

SP - 1131

EP - 1144

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 5

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this