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

Abstract

Let M be a Hopf hypersurface in a nonflat complex space form , , 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].

Nonexistence of non-Hopf Ricci-semisymmetric real hypersurfaces in and

“…Thus, combining with Theorem 1.1, we have shown that there do not exist non-Hopf hypersurfaces in with recurrent Ricci tensor. Finally, we noticed that very recently Wang [21] studied Ricci -recurrent real hypersurfaces in .…”