论文标题
正常雅各比操作员在复杂四边形中真实超曲面上的衍生物
Derivatives of normal Jacobi operator on real hypersurfaces in the complex quadric
论文作者
论文摘要
在\ cite {s 2017}中，suh给出了与平行的正常雅各比运算符在复杂四边形中的hopf真实超曲面的不存在定理。在本文中，我们介绍了一些普遍的条件，称为$ \ Mathcal C $ - 平行或REEB并行普通雅各比运算符。通过使用普通雅各比操作员的这种较弱的并行性，首先，我们可以在复杂的四边形$ q^{m} $，$ m \ m \ geq 3 $中，用$ \ mathcal c $ - 平行的jacobi jacobi操作员来主张hopf真实超曲面的不存在定理。接下来，我们证明，当且仅当它具有$ \ mathfrak a $ - 异位单数奇异的正常矢量字段时，就会证明HOPF真实的HyperSurface具有REEB并行普通Jacobi操作员。
In \cite{S 2017}, Suh gave a non-existence theorem for Hopf real hypersurfaces in the complex quadric with parallel normal Jacobi operator. Motivated by this result, in this paper, we introduce some generalized conditions named $\mathcal C$-parallel or Reeb parallel normal Jacobi operators. By using such weaker parallelisms of normal Jacobi operator, first we can assert a non-existence theorem of Hopf real hypersurfaces with $\mathcal C$-parallel normal Jacobi operator in the complex quadric $Q^{m}$, $m \geq 3$. Next, we prove that a Hopf real hypersurface has Reeb parallel normal Jacobi operator if and only if it has an $\mathfrak A$-isotropic singular normal vector field.
