单位球面中具有3个不同Blaschke特征值的Blaschke平行子流形  

On the Blaschke Parallel Submanifolds in the Unit Sphere with Three Distinct Blaschke Eigenvalues

作　　者：李兴校[1] 宋虹儒 LI Xingxiao;SONG Hongru(School of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,Henan,China;pingyuan Foreign Language School,Xinxiang 453500,Henan,China)

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007 [2]新乡市平原外国语学校,河南新乡453500

出　　处：《数学年刊（A辑）》2018年第3期249-272,共24页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11671121;No.11171091;No.11371018)的资助

摘　　要：Blaschke张量A是单位球面S^n中子流形的M?bius微分几何的一个基本不变量,而A的特征值称为Blaschke特征值.作者研究了S^n中具有平行Blaschke张量的子流形(简称为Blaschke平行子流形).主要结果是对S^n中具有3个不同Blaschke特征值的Blaschke平行子流形进行了完全的分类.As is known, the Blaschke tensor A （a symmetric covariant 2-tensor） is one of the fundamental MSbius invariants in the MSbius differential geometry of submanifolds in the unit sphere Sn, and the eigenvalues of A are referred to as the Blaschke eigenvalues. This paper deals with the submanifolds in Sn with parallel Blaschke tensor which are called Blaschke paraltel submanifolds. The main theorem of this paper is the classification of Blaschke parallel submanifolds in Sn with exactly three distinct Blaschke eigenvalues.

关 键 词：平行Blaschke张量 消失的Mobius形式 常数量曲率 平行平均曲率向量 

分 类 号：O186.1[理学—数学]