On Hopf hypersurfaces in a non-flat complex space form with η-recurrent Ricci tensor

Abstract

Baikoussis, Lyu and Suh [1] showed that a Hopf hypersurface M in a non-flat complex space form M_n(c) with constant mean curvature and with η-recurrent Ricci tensor is locally congruent to one of real hypersurfaces of type A and B. They also conjectured that the same result can be obtained even without the constancy assumption on the mean curvature (cf. [1, Remark 5.1.]). The purpose of this paper is to answer this question in the affirmative.