Hypersurfaces with Isotropic Para-Blaschke Tensor  

作　　者：Jian Bo FANG Kun ZHANG 

机构地区：[1]Department of Mathematics and Statistics,Chuxiong Normal University

出　　处：《Acta Mathematica Sinica,English Series》2014年第7期1195-1209,共15页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.10861013);Academic Talents of Chuxiong Normal University(Grant No.09YJRC10)

摘　　要：Let Mn be an n-dimensional submanifold without umbilical points in the （n ＋ 1）-dimen- sional unit sphere Sn＋l. Four basic invariants of Mn under the Moebius transformation group of Sn＋1 are a 1-form Ф called moebius form, a symmetric （0, 2） tensor A called Blaschke tensor, a symmetric （0, 2） tensor B called Moebius second fundamental form and a positive definite （0, 2） tensor g called Moebius metric. A symmetric （0,2） tensor D = A ＋ μB called para-Blaschke tensor, where μ is constant, is also an Moebius invariant. We call the para-Blaschke tensor is isotropic if there exists a function ,λ such that D = λg. One of the basic questions in Moebius geometry is to classify the hypersurfaces with isotropic para-Blaschke tensor. When λ is not constant, all hypersurfaces with isotropic para-Blaschke tensor are explicitly expressed in this paper.Let Mn be an n-dimensional submanifold without umbilical points in the （n ＋ 1）-dimen- sional unit sphere Sn＋l. Four basic invariants of Mn under the Moebius transformation group of Sn＋1 are a 1-form Ф called moebius form, a symmetric （0, 2） tensor A called Blaschke tensor, a symmetric （0, 2） tensor B called Moebius second fundamental form and a positive definite （0, 2） tensor g called Moebius metric. A symmetric （0,2） tensor D = A ＋ μB called para-Blaschke tensor, where μ is constant, is also an Moebius invariant. We call the para-Blaschke tensor is isotropic if there exists a function ,λ such that D = λg. One of the basic questions in Moebius geometry is to classify the hypersurfaces with isotropic para-Blaschke tensor. When λ is not constant, all hypersurfaces with isotropic para-Blaschke tensor are explicitly expressed in this paper.

关 键 词：Moebius geometry para-Blaschke tensor ISOTROPIC 

分 类 号：O183.2[理学—数学]