On a real hypersurface M of a complex quadric we have an almost contact metric structure induced by the Kählerian structure of the ambient space. Therefore, on M we have the Levi-Civita connection \(\nabla \) and, for any non-null real number k, the so called kth generalized Tanaka Webster connection \({\hat{\nabla }}^{(k)}\). We introduce the notions of \(({\hat{\nabla }}^{(k)},\nabla )\)-Codazzi and \(({\hat{\nabla }}^{(k)},\nabla )\)-Killing normal Jacobi operator on such a real hypersurface and classify Hopf real hypersurface in a complex quadric whose normal Jacobi operators satisfy any of both conditions.

在复杂二次曲面的实超曲面M上，我们具有由环境空间的Kählerian结构引起的几乎接触的度量结构。因此，在M上，我们具有Levi-Civita连接\（\ nabla \），对于任何非空实数k，所谓的k th广义Tanaka Webster连接\（{\ hat {\ nabla}} ^ {（ k）} \）。我们介绍\（（{{hat {\ nabla}} ^ {（k）}，\ nabla）\）- Codazzi和\（（{{hat {\ nabla}} ^ {（k）}，\ nabla）\）-在这样的实超曲面上杀死普通Jacobi算符，并在其普通Jacobi算符满足两个条件中任意一个的复二次曲面中对Hopf实超曲面分类。