CHARACTERIZATIONS OF REAL HYPERSURFACES OF COMPLEX SPACE FORMS IN TERMS OF RICCI OPERATORS

Abstract

We prove that a real hypersurface M in a complex space form Mn(c), <TEX>$c{\neq}0$</TEX>, whose Ricci operator and structure tensor commute each other on the holomorphic distribution and the Ricci operator is <TEX>${\eta}-parallel$</TEX>, is a Hopf hypersurface. We also give a characterization of this hypersurface.