Willmore hypersurfaces with vanishing Möbius form in S4

Tongzhu Li; Bingxin Xie

doi:10.1142/S0129167X26500151

Willmore hypersurfaces with vanishing Möbius form in S⁴

Tongzhu Li^*
, Bingxin Xie

^*Corresponding author for this work

Beijing Institute of Technology

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

Abstract

Let x: Mⁿ → Sⁿ⁺¹ be an immersed hypersurface without umbilical points, one can define the Möbius metric g and the Möbius form C, which are invariant under the Möbius transformation group of Sⁿ⁺¹. A hypersurface is called a Willmore hypersurface if it is the critical point of the volume functional of Mⁿ with respect to the Möbius metric g. In this paper, we classify completely the Willmore hypersurfaces with vanishing Möbius form (i.e.

Original language	English
Article number	2650015
Journal	International Journal of Mathematics
Volume	37
Issue number	2
DOIs	https://doi.org/10.1142/S0129167X26500151
Publication status	Accepted/In press - 2025
Externally published	Yes

Keywords

Möbius form
Möbius metric
Willmore hypersurface
minimal hypersurface

Access to Document

10.1142/S0129167X26500151

Cite this

@article{f17935359deb46ad8e5c07ddb072c05f,

title = "Willmore hypersurfaces with vanishing M{\"o}bius form in S4",

abstract = "Let x: Mn → Sn+1 be an immersed hypersurface without umbilical points, one can define the M{\"o}bius metric g and the M{\"o}bius form C, which are invariant under the M{\"o}bius transformation group of Sn+1. A hypersurface is called a Willmore hypersurface if it is the critical point of the volume functional of Mn with respect to the M{\"o}bius metric g. In this paper, we classify completely the Willmore hypersurfaces with vanishing M{\"o}bius form (i.e.",

keywords = "M{\"o}bius form, M{\"o}bius metric, Willmore hypersurface, minimal hypersurface",

author = "Tongzhu Li and Bingxin Xie",

note = "Publisher Copyright: {\textcopyright} 2026 World Scientific Publishing Company.",

year = "2025",

doi = "10.1142/S0129167X26500151",

language = "English",

volume = "37",

journal = "International Journal of Mathematics",

issn = "0129-167X",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "2",

}

TY - JOUR

T1 - Willmore hypersurfaces with vanishing Möbius form in S4

AU - Li, Tongzhu

AU - Xie, Bingxin

PY - 2025

Y1 - 2025

N2 - Let x: Mn → Sn+1 be an immersed hypersurface without umbilical points, one can define the Möbius metric g and the Möbius form C, which are invariant under the Möbius transformation group of Sn+1. A hypersurface is called a Willmore hypersurface if it is the critical point of the volume functional of Mn with respect to the Möbius metric g. In this paper, we classify completely the Willmore hypersurfaces with vanishing Möbius form (i.e.

AB - Let x: Mn → Sn+1 be an immersed hypersurface without umbilical points, one can define the Möbius metric g and the Möbius form C, which are invariant under the Möbius transformation group of Sn+1. A hypersurface is called a Willmore hypersurface if it is the critical point of the volume functional of Mn with respect to the Möbius metric g. In this paper, we classify completely the Willmore hypersurfaces with vanishing Möbius form (i.e.

KW - Möbius form

KW - Möbius metric

KW - Willmore hypersurface

KW - minimal hypersurface

UR - https://www.scopus.com/pages/publications/105024106065

U2 - 10.1142/S0129167X26500151

DO - 10.1142/S0129167X26500151

M3 - Article

AN - SCOPUS:105024106065

SN - 0129-167X

VL - 37

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 2

M1 - 2650015

ER -

Willmore hypersurfaces with vanishing Möbius form in S⁴

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this