Certain Characterization of Real Hypersurfaces of type A in a Nonflat Complex Space Form

Let M be a real hypersurface with almost contact metric structure (phi, xi, eta, g) in a nonflat complex space form M-n (c). We denote S and F4 by the R-xi tensor of M and by the structure Jacobi operator with respect to the vector field xi respectively. In this paper, we prove that M is a Hopf hypersurface of type A in M-n(c) if it satisfies F-xi phi = phi R-xi and at the same time R-xi (S phi - phi S) = 0.