We want to treat this problem for real hypersurfaces in a complex hyperbolic space $J_n(C)$. Thus it seems to be natural to consider some problems concerned with the estimation of the Ricci tensor for real hypersurfaces in $H_n(C)$<TEX>. In this paper we will find a new tensorial formula concerned with the Ricci tensor and give it a characterization of horospheres and geodesic hyperspheres in a complex hyperbolic space <TEX>$H_n(C)$<TEX>.