李兴校,宋虹儒.单位球面中具有3个不同 Blaschke 特征值的 Blaschke 平行子流形[J].数学年刊A辑,2018,39(3):249~272
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
Received: April 29, 2016  Revised: March 21, 2017
DOI:10.16205/j.cnki.cama.2018.0023
中文关键词:  平行 Blaschke 张量, 消失的 mo 形式, 常 数量曲率, 平行 平均曲率向量
英文关键词:Parallel Blaschke tensor, Vanishing mo form, Constant scalar curvature, Parallel mean curvature vector
基金项目:本文受到国家自然科学基金(No.11671121, No.11171091, No.11371018)的资助.
Author NameAffiliationE-mail
LI Xingxiao School of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, China. xxl@henannu.edu.cn 
SONG Hongru Pingyuan Foreign Language School, Xinxiang 453500, Henan, China. yaozheng-shr@163.com 
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中文摘要:
      Blaschke 张量 $A$ 是单位球面 $\bbs^n$中子流形的 \mo 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$\bbs^n$ 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 $\bbs^n$ 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.
英文摘要:
      As is known, the Blaschke tensor $A$ (a symmetric covariant $2$-tensor) is one of the fundamental \mo invariants in the \mo differential geometry of submanifolds in the unit sphere $\bbs^n$, and the eigenvalues of $A$ are referred to as the Blaschke eigenvalues. This paper deals with the submanifolds in $\bbs^n$ with parallel Blaschke tensor which are called Blaschke parallel submanifolds. The main theorem of this paper is the classification of Blaschke parallel submanifolds in $\bbs^n$ with exactly three distinct Blaschke eigenvalues.
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