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Ricci η‐recurrent real hypersurfaces in 2‐dimensional nonflat complex space forms
Mathematische Nachrichten ( IF 0.8 ) Pub Date : 2020-09-28 , DOI: 10.1002/mana.201800474
Yaning Wang 1
Affiliation  

Let M be a Hopf hypersurface in a nonflat complex space form M 2 ( c ) , c 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

M为非平面复空间形式的Hopf超曲面 中号 2 C C 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。
更新日期:2020-09-28
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