A study of real hypersurfaces with Ricci operators in 2-dimensional complex space forms

We prove that a real hypersurface M in complex projective space P 2 ‫)ރ(‬ or complex hyperbolic space H 2 ‫,)ރ(‬ whose Ricci operator is η-parallel and commutes with the structure tensor on the holomorphic distribution, is a Hopf hypersurface.We also give a characterization of this hypersurface.