Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (1): 35-42.

Previous Articles     Next Articles

Spectral Geometry of Willmore and Extremal Hypersurfaces

Yang Dengyun1,*,Zhang Jinguo1(),Tao Yongqian2()   

  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)


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 $C_{m,m}$).

Key words: Spectrum, Laplace operator, Extremal hypersurface, Willmore hypersurface, The second fundamental form

CLC Number: 

  • O186.12