Suh (Math. Nachr. 290 (2017) 442–451) proved that there are no Hopf real hypersurfaces in the complex quadric that have parallel normal Jacobi operators. Motivated by this result, in this paper, we introduce the notions of $\mathcal{C}$‐parallel and Reeb parallel for normal Jacobi operators, which generalize the notion ‘parallel’. First we obtain a non‐existence theorem of Hopf real hypersurfaces with $\mathcal{C}$‐parallel normal Jacobi operator in the complex quadric $Q^m$ for $m⩾3$. We then prove that a Hopf real hypersurface has a Reeb parallel normal Jacobi operator if and only if it has an $\mathfrak{A}$‐isotropic singular normal vector field.

中文翻译：

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复二次曲面上实超曲面上的正常Jacobi算子的导数

徐（数学式的nAChR。290（2017）442-451）证明，有在复二次没有真正的Hopf超曲面具有平行正常雅可比符。受此结果的启发，在本文中，我们介绍了$\mathcal{C}$-并行和Reeb并行，适用于常规Jacobi运算符，这些概念推广了“并行”概念。首先，我们获得具有以下条件的Hopf实超曲面的不存在性定理：$\mathcal{C}$-复二次曲面上的-平行标准Jacobi算子 ${问}^{米}$ 对于 $米⩾3$。然后，我们证明Hopf实超曲面在且仅当具有一个Reeb平行法线Jacobi算符$\mathfrak{一种}$各向同性奇异法向矢量场。