关于$\mathbb{C}P^3$ 中的伪脐Lagrange子流形

On Pseudo-Umbilical Lagrangian Submanifolds in $\mathbb{C}P^3$

中文关键词:  伪脐子流形  Lagrange子流形  数量曲率  平均曲率

英文关键词:pseudo-umbilical submanifolds  Lagrangian submanifolds  scalar curvature  mean curvature.

中文摘要:

      本文获得$\mathbb{C}P^3$中非极小的紧致伪脐Lagrange子流形常数数量曲率的一个估计. 作为其应用, 我们证明了$\mathbb{C}P^3$中紧致Einstein伪脐Lagrange子流形必是极小的.

英文摘要:

      In this paper, an estimate of the constant scalar curvature of a compact non-minimal pseudo-umbilical Lagrangian submanifold in $\mathbb{C}P^3$ is obtained. As its application, we prove that compact Einstein pseudo-umbilical Lagrangian submanifolds in $\mathbb{C}P^3$ must be minimal.