论文标题
在复杂的Quadric中，将Jacobi操作员通勤在B型的真实超曲面上
Commuting Jacobi operators on Real hypersurfaces of Type B in the complex quadric
论文作者
论文摘要
在本文中，首先，我们研究了普通的雅各比操作员〜$ {\ bar r} _n $与jacobi操作员的结构〜$r_ξ$ for hopf for hopf for hopf for hopf for hopf for hopf confepples〜$ q^m = so_ = so_ so_ {m+2}} r_ξ=r_ξ{\ bar r} _n $。此外，获得了$ \ mathfrak的HOPF真实超曲面的新表征，在复杂的四边形〜$ q^{m} $中，获得了$ - 原理单数正常矢量场。借助此结果，我们可以通过通勤Jacobi运算符在复杂的四边形〜$ q^{m} $中对HOPF真实的超曲面进行显着分类。
In this paper, first, we investigate the commuting property between the normal Jacobi operator~${\bar R}_N$ and the structure Jacobi operator~$R_ξ$ for Hopf real hypersurfaces in the complex quadric~$Q^m = SO_{m+2}/SO_mSO_2$, $m \geq 3$, which is defined by ${\bar R}_N R_ξ = R_ξ{\bar R}_N$. Moreover, a new characterization of Hopf real hypersurfaces with $\mathfrak A$-principal singular normal vector field in the complex quadric~$Q^{m}$ is obtained. By virtue of this result, we can give a remarkable classification of Hopf real hypersurfaces in the complex quadric~$Q^{m}$ with commuting Jacobi operators.
