If we consider a real hypersurface M in a complex projective space we have the covariant derivatives associated to both the Levi-Civita connection and, for any nonnull real number k, to the k-th generalized Tanaka-Webster connection. We also have the Lie derivative and a derivative of Lie type associated to the k-th generalized Tanaka-Webster connection. If we consider the structure Lie operator \(L_{\xi }\) on M, we can define two tensor fields of type (1,2) on M from \(L_{\xi }\) associated to the derivatives mentioned above, \(L_{{\xi }_F}^{(k)}\) and \(L_{{\xi }_T}^{(k)}\). Kaimakamis, Panagiotidou and Pérez obtained the classifications of real hypersurfaces for which either \(L_{{\xi }_F}^{(k)}\) or \(L_{{\xi }_T}^{(k)}\) identically vanish. We generalize such results classifying real hypersurfaces in complex projective space such that \(L_{{\xi }_F}^{(k)}\) (respectively, \(L_{{\xi }_T}^{(k)}\)) is either symmetric or skew symmetric.

如果我们考虑复射影空间中的实超曲面M，我们有与 Levi-Civita 连接相关联的协变导数，对于任何非零实数k，与第k个广义 Tanaka-Webster 连接相关联。我们还有与第k个广义 Tanaka-Webster 连接相关联的 Lie 导数和 Lie 类型的导数。如果我们考虑到结构烈操作者\（L _ {\ XI} \）上中号，我们可以定义类型（1,2）的2个量场中号从\（L _ {\ XI} \）关联到所述衍生物上述, \(L_{{\xi }_F}^{(k)}\)和\(L_{{\xi }_T}^{(k)}\). Kaimakamis、Panagiotidou 和 Pérez 获得了真实超曲面的分类，其中\(L_{{\xi }_F}^{(k)}\)或\(L_{{\xi }_T}^{(k)}\ )同样消失。我们概括了这样的结果，即在复杂的投影空间中对真实超曲面进行分类，使得\(L_{{\xi }_F}^{(k)}\)（分别为\(L_{{\xi }_T}^{(k)} \) ) 是对称的或倾斜对称的。