Jacobi Operators with Respect to the Reeb Vector Fields on Real Hypersurfaces in a Nonflat Complex Space Form

Abstract

Let M be a real hypersurface of a complex space form with almost contact metric structure (φ, ξ, η, g). In this paper, we prove that if the structure Jacobi operator Rξ = R(·, ξ)ξ is φ∇ξξ-parallel and Rξ commute with the structure tensor φ, then M is a homogeneous real hypersurface of Type A provided that TrRξ is constant.