Ricci η‐recurrent real hypersurfaces in 2‐dimensional nonflat complex space forms

Yaning Wang

Mathematische Nachrichten, 2021, vol. 294, issue 1, 195-206

Abstract: Let M be a Hopf hypersurface in a nonflat complex space form M2(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].

Date: 2021
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https://doi.org/10.1002/mana.201800474

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