Real hypersurfaces in complex two-plane Grassmannians with commuting Ricci tensor

In this paper, first we introduce the full expression for the Ricci tensor of a real hypersurface MM in complex two-plane Grassmannians G2(Cm+2)G2(Cm+2) from the equation of Gauss. Next we prove that a Hopf hypersurface in complex two-plane Grassmannians G2(Cm+2)G2(Cm+2) with commuting Ricci tensor is locally congruent to a tube of radius rr over a totally geodesic G2(Cm+1)G2(Cm+1). Finally it can be verified that there do not exist any Hopf Einstein hypersurfaces in G2(Cm+2)G2(Cm+2).