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

Abstract

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 \({\nabla_{\phi\nabla_{\xi}\xi}S = 0}\) . Under some further conditions we characterize Hopf hypersurfaces of \({P_{n}\mathbb{C}}\) .