Structure Jacobi Operators of Real Hypersurfaces with Constant Mean Curvature in a Complex Space Form

Abstract

Let M be a real hypersurface with constant mean curvature in a complex space form Mn(c), c ̸= 0. In this paper, we prove that if the structure Jacobi operator Rξ = R(·, ξ)ξ with respect to the structure vector field ξ is φ∇ξξ-parallel and Rξ commute with the structure tensor field φ, then M is a homogeneous real hypersurface of Type A.