Abstract In this paper, we introduce a notion of generalized Killing shape operator (or called the quadratic Killing shape operator) and its geometric meaning on real hypersurfaces in the complex quadric. In addition, we give a non-existence theorem for a Hopf real hypersurface with generalized Killing shape operator in the complex quadric.

中文翻译：

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具有广义杀戮形状算子的复二次曲面中的真实超曲面

摘要 在本文中，我们介绍了广义Killing 形状算子（或称为二次Killing 形状算子）的概念及其在复二次曲面的真实超曲面上的几何意义。此外，我们给出了复二次曲面中具有广义 Killing 形状算子的 Hopf 实超曲面的不存在定理。