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### Willmore超曲面与极值超曲面的谱特征

1. 1江西师范大学数学与统计学院 南昌 330022
2南昌大学数学系 南昌 330031
• 收稿日期:2021-11-24 修回日期:2022-10-17 出版日期:2023-02-26 发布日期:2023-03-07
• 通讯作者: *杨登允, E-mail: yangdengyun@139.com
• 作者简介:张金国, E-mail: jgzhang@jxnu.edu.cn|陶永芊, E-mail: taoyongqian@ncu.edu.cn
• 基金资助:
国家自然科学基金(12061036);国家自然科学基金(11761049);江西省自然科学基金重点项目(20202ACB201001)

### Spectral Geometry of Willmore and Extremal Hypersurfaces

Dengyun Yang1,*,Jinguo Zhang1(),Yongqian Tao2()

1. 1School of Mathematics and Statistic, Jiangxi Normal University, Nanchang 330022
2Department of Mathematics, Nanchang University, Nanchang 330031
• Received:2021-11-24 Revised:2022-10-17 Online:2023-02-26 Published:2023-03-07
• Supported by:
National Natural Science Foundation of China(12061036);National Natural Science Foundation of China(11761049);Jiangxi Provincial Natural Science Foundation(20202ACB201001)

$M$ 为单位球面 $S^{n+1}$ 中的Willmore超曲面(或极值超曲面). 该文证明了, 若 $M$ 与Willmore环面 $W_{m,n-m}$ (或Clifford环面$C_{m,n-m}$)具有相同的第二基本形式模长, 并且 $Spec^p(M)=Spec^p(W_{m,n-m})$ (或$Spec^p(M)=Spec^p(C_{m,n-m})$),其中 $p=0,1,2$, 则有 $M=W_{m,n-m}$ (或$M=C_{m,m}$).

Abstract:

Let $M$ be a Willmore (or extremal) hypersurface in $S^{n+1}$ with the same squared length of the second fundamental form of Willmore torus $W_{m,n-m}$ (or Clifford torus $C_{m,n-m}$). In this article the authors proved that if $Spec^p(M)=Spec^p(W_{m,n-m})$ (or $Spec^p(M)=Spec^p(C_{m,n-m})$) for $p=0,1,2$, then $M$ is $W_{m,n-m}$ (or $C_{m,m}$).

• O186.12