Real hypersurfaces in a complex space form with non-commuting operators

Let M   be a real hypersurface with almost contact metric structure (ϕ,g,ξ,η)(ϕ,g,ξ,η) in a complex space form Mn(c)Mn(c), c≠0c≠0. In this paper we prove that if RξϕA+AϕRξ=0RξϕA+AϕRξ=0 holds on M, then M   is a Hopf hypersurface in Mn(c)Mn(c), where A denotes the shape operator, ϕ   the structure tensor and RξRξ the Jacobi operator with respect to the structure vector field ξ  . We characterize such Hopf hypersurfaces of Mn(c)Mn(c).