THE RICCI TENSOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS Perez Juan De Dios; Suh Young-Jin;
In this paper, first we introduce the full expression of the curvature tensor of a real hypersurface M in complex two-plane Grass-mannians from the equation of Gauss and derive a new formula for the Ricci tensor of M in . Next we prove that there do not exist any Hopf real hypersurfaces in complex two-plane Grassmannians with parallel and commuting Ricci tensor. Finally we show that there do not exist any Einstein Hopf hypersurfaces in .
real hypersurfaces;complex two-plane Grassmannians;parallel Ricci tensor;commuting Ricci tensor;Einstein;