Conditions of Parallelism of $^{*}$-Ricci Tensor of Three Dimensional Real Hypersurfaces in Non-flat Complex Space Forms

Abstract

This paper focuses on the study of three dimensional real hypersurfaces in non-flat complex space forms whose $^{*}$-Ricci tensor satisfies conditions of parallelism. More precisely, results concerning real hypersurfaces with vanishing, semi-parallel and pseudo-parallel $^{*}$-Ricci tensor in complex hyperbolic space are provided. Furthermore, new results concerning $\xi$-parallelism of $^{*}$-Ricci tensor of real hypersurfaces in non-flat complex space forms are presented.