REAL HYPERSURFACES WITH ξ-PARALLEL RICCI TENSOR IN A COMPLEX SPACE FORM

We prove that if a real hypersurface with constant mean curvature of a complex space form satisfying ▽$_{ξ/}$S = 0 and Sξ = $\sigma$ξ for a smooth function $\sigma$, then the structure vector field ξ is principal, where S denotes the Ricci tensor of the hypersurface.