| 单位球面中具有3个不同 Blaschke 特征值的 Blaschke 平行子流形 |
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| 引用本文： | 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(中文版),2018,39(3):249-272. |
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| 作者姓名： | 李兴校 宋虹儒 |
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| 作者单位： | 河南师范大学数学与信息科学学院;新乡市平原外国语学校 |
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| 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. |
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| 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.
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| 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 |
| 收稿时间： | 2016/4/29 0:00:00 |
| 修稿时间： | 2017/3/21 0:00:00 |
On the Blaschke Parallel Submanifolds in the Unit Sphere with Three Distinct Blaschke Eigenvalues |
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| LI Xingxiao and SONG Hongru.On the Blaschke Parallel Submanifolds in the Unit Sphere with Three Distinct Blaschke Eigenvalues[J].Chinese Annals of Mathematics,2018,39(3):249-272. |
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| Authors: | LI Xingxiao and SONG Hongru |
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| Institution: | School of Mathematics and Information Science, Henan Normal University,
Xinxiang 453007, Henan, China. and Pingyuan Foreign Language School, Xinxiang 453500, Henan, China. |
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| Abstract: | 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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| Keywords: | Parallel Blaschke tensor Vanishing mo form Constant scalar curvature Parallel mean curvature vector |
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