球空间中一类新的Willmore型超曲面的Simons型定理
Simons-Type Inequality on a New Class of Willmore-Type Hypersurfaces in Spheres
钟景洋 1楼文晓1
作者信息
- 1. 福州大学数学与统计学院,福建 福州 350108
- 折叠
摘要
主旨是在一般维数球面中的闭超曲面上构造一类泛函Tn作为Willmore泛函的推广.我们将证明Tn和原始Willmore泛函具有类似的性质,即Tn是共形不变的,并且当n为偶数时,Tn对应的变分极小闭超曲面同样满足Simons型不等式,这说明Tn-极小闭超曲面具有某种几何刚性.
Abstract
In the paper,we define a class of functionals Tn of hypersurfaces in general dimensional spheres as generation of Willmore functionals.We will prove that Tn have similar properties as Willmore functionals,that is to say,Tn are always conformal invariants,when n is even,the Tn-critical closed hypersurfaces also satisfy Simons-type inequalities,which shows that Tn-critical closed hypersurfaces have sort of rigidity in geometry.
关键词
共形几何/共形不变量/Willmore泛函/Simons不等式Key words
conformal geometry/conformal invariants/Willmore functional/Simons in-equality引用本文复制引用
基金项目
福建省中青年教师教育科研资助项目(JAT1900018)
出版年
2024
NETL
NSTL
万方数据