Willmore超曲面与极值超曲面的谱特征

Spectral Geometry of Willmore and Extremal Hypersurfaces

设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)).

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)).