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

Let $M$ be a real hypersurface of a complex space form with almostcontact metric structure $(\phi, \xi, \eta, g)$. In this paper, weprove that if the structure Jacobi operator $R_\xi=R(\cdot,\xi)\xi$ is$\phi\nabla_{\xi} \xi$-parallel and $R_{\xi}$ commute with thestructure tensor $\phi$, then $M$ is a homogeneous real hypersurface ofType A provided that Tr$R_{\xi}$ is constant. KCI Citation Count: 2