数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 35-42.

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Willmore超曲面与极值超曲面的谱特征

杨登允1,*,张金国1(),陶永芊2()   

  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

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)

摘要:

M 为单位球面 Sn+1 中的Willmore超曲面(或极值超曲面). 该文证明了, 若 M 与Willmore环面 Wm,nm (或Clifford环面Cm,nm)具有相同的第二基本形式模长, 并且 Specp(M)=Specp(Wm,nm) (或Specp(M)=Specp(Cm,nm)),其中 p=0,1,2, 则有 M=Wm,nm (或M=Cm,m).

关键词: 拉普拉斯算子, 谱, Willmore超曲面, 极值超曲面, 第二基本形式

Abstract:

Let M be a Willmore (or extremal) hypersurface in Sn+1 with the same squared length of the second fundamental form of Willmore torus Wm,nm (or Clifford torus Cm,nm). In this article the authors proved that if Specp(M)=Specp(Wm,nm) (or Specp(M)=Specp(Cm,nm)) for p=0,1,2, then M is Wm,nm (or Cm,m).

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

中图分类号: 

  • O186.12