The Ricci tensor and structure Jacobi operator of real hypersurfaces in a complex projective space

Let M be a real hypersurface with almost contact metric structure ${(phi, xi, eta, g)}$ in a complex projective space ${P_{n}mathbb{C}}$ . A Real hypersurface M is said to be a Hopf hypersurface if ξ is principal. In this paper we investigate real hypersurfaces of ${P_{n}mathbb{C}}$ whose Ricci tensors S satisfy ${nabla_{phinabla_{xi}xi}S = 0}$ . Under some further conditions we characterize Hopf hypersurfaces of ${P_{n}mathbb{C}}$ .