e???-recurrent a??-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms

摘要

Kaimakamis and Panagiotidou in [Taiwanese J. Math. 18(6) (2014), 1991a??1998] proposed an open question: are there real hypersurfaces in nonflat complex space forms whose a??-Ricci tensor satisfies the condition of e???-parallelism? In this short note, we present an affirmative answer and prove that a three-dimensional real hypersurface in a nonflat complex space form has e???-parallel a??-Ricci tensor if and only if it is locally congruent to either a geodesic hypersphere of radius r in a?? H2(c) with tanha??(|c|2r)=12 or a ruled real hypersurface.