Pseudo-Einstein real hypersurfaces in complex hyperbolic two-plane Grassmannians

In this paper we first introduce the full expression of the curvature tensor of a real hypersurface M   in complex hyperbolic two-plane Grassmannians SU2,m/S(U2⋅Um)SU2,m/S(U2⋅Um), m≥2m≥2 from the equations of Gauss. Next we derive a new formula for the Ricci tensor of M   in SU2,m/S(U2⋅Um)SU2,m/S(U2⋅Um). As an application of this result we prove that there do not exist Einstein Hopf or Q⊥Q⊥-invariant Einstein real hypersurfaces in SU2,m/S(U2⋅Um)SU2,m/S(U2⋅Um).