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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.

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