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

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.
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.