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

作　　者：钟景洋 楼文晓 ZHONG Jing-yang;LOU Wen-xiao(College of Mathematics and Statistics,Fuzhou University,Fuzhou 350108,China)

机构地区：[1]福州大学数学与统计学院,福建福州350108

出　　处：《数学的实践与认识》2024年第10期178-185,共8页Mathematics in Practice and Theory

基　　金：福建省中青年教师教育科研资助项目(JAT1900018)。

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T_(n)作为Willmore泛函的推广,我们将证明T_(n)和原始Willmore泛函具有类似的性质,即T_(n)是共形不变的,并且当n为偶数时,T_(n)对应的变分极小闭超曲面同样满足Simons型不等式,这说明T_(n)-极小闭超曲面具有某种几何刚性。In the paper,we define a class of functionals T_(n) of hypersurfaces in general dimensional spheres as generation of Willmore functionals.We will prove that T_(n) have similar properties as Willmore functionals,that is to say,T_(n) are always conformal invariants,when n is even,the T_(n)-critical closed hypersurfaces also satisfy Simons-type inequalities,which shows that T_(n)-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 

分 类 号：O186.1[理学—数学]