ON THE STRUCTURE JACOBI OPERATOR AND RICCI TENSOR OF REAL HYPERSURFACES IN NONFLAT COMPLEX SPACE FORMS

Abstract

It is known that there are no real hypersurfaces with parallel structure Jacobi operator <TEX>$R_{\xi}$</TEX> (cf.[16], [17]). In this paper we investigate real hypersurfaces in a nonflat complex space form using some conditions of the structure Jacobi operator <TEX>$R_{\xi}$</TEX> which are weaker than <TEX>${\nabla}R_{\xi}$</TEX> = 0. Under further condition <TEX>$S\phi={\phi}S$</TEX> for the Ricci tensor S we characterize Hopf hypersurfaces in a complex space form.