Let M be a Hopf hypersurface in a nonflat complex space form $M^2(c)$, $c\ne 0$, of complex dimension two. In this paper, we prove that M has η‐recurrent Ricci operator if and only if it is locally congruent to a homogeneous real hypersurface of type (A) or (B) or a non‐homogeneous real hypersurface with vanishing Hopf principal curvature. This is an extension of main results in [17, 21] for real hypersurfaces of dimension three. By means of this result, we give some new characterizations of Hopf hypersurfaces of type (A) and (B) which generalize those in [14, 18, 26].

中文翻译：

---

二维非平面复空间形式的Ricciη递归实超曲面

令M为非平面复空间形式的Hopf超曲面${\mathrm{中号}}^2（C）$， $C\ne 0$，维度为2。在本文中，我们证明M具有η-递归Ricci算子，且仅当它与（A）或（B）类型的同构实超曲面或具有不相同的Hopf主曲率的非均匀实超曲面局部一致时。这是[17，21]中关于三维三维实际超曲面的主要结果的扩展。通过该结果，我们给出了（A）和（B）类型的Hopf超曲面的一些新特征，这些特征概括了[14、18、26]中的特征。