Abstract In this paper, we introduce a new notion of quadratic Killing normal Jacobi operator (simply, Killing normal Jacobi operator) and its geometric meaning for real hypersurfaces in the complex Grassmannians of rank two G 2 m + 2 ( c ) , c ≠ 0 . In addition, we give two classification theorems for Hopf real hypersurfaces with quadratic Killing normal Jacobi operator in complex two-plane Grassmannians of compact type and of non-compact type.

中文翻译：

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2 阶复杂 Grassmannians 中真实超曲面的 Quadratic Killing normal Jacobi 算子

摘要 在本文中，我们介绍了二次杀死法线雅可比算子的新概念（简称为杀死法线雅可比算子）及其在阶数为 G 2 m + 2 ( c ) , c ≠ 0 的复格拉斯曼数中的实超曲面的几何意义. 此外，我们给出了具有二次Killing normal Jacobi算子的Hopf实超曲面在紧型和非紧型复双平面Grassmannians中的两个分类定理。