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, extension of existing results concerning real hypersurfaces with vanishing, semi-parallel and pseudo-parallel $^{*}$-Ricci tensor in case of ambient space being the 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.