Real hypersurfaces in complex two-plane Grassmannians with ξ-invariant Ricci tensor

In this paper, first we introduce the full expression of the Ricci tensor of a real hypersurface M in complex two-plane Grassmannians G2(Cm+2) from the equation of Gauss. Next, we give a new characterization of real hypersurfaces of type (A) in complex two-plane Grassamnnians with a vanishing Lie derivative of the Ricci tensor S in the direction of the Reeb vector field ξ, that is, an ξ-invariant Ricci tensor.