%0 Journal Article
%T Jacobi operators along the structure flow on real hypersurfaces in a nonflat complex space form
%A U-Hang Ki
%A Hiroyuki Kurihara
%A Ryoichi Takagi
%J Mathematics
%D 2007
%I arXiv
%X Let $M$ be a real hypersurface of a complex space form with almost contact metric structure $(\phi, \xi, \eta, g)$. In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_\xi=R(\cdot,\xi)\xi$ is $\xi$-parallel. In particular, we prove that the condition $\nabla_{\xi} R_{\xi}=0$ characterizes the homogeneous real hypersurfaces of type $A$ in a complex projective space or a complex hyperbolic space when $R_{\xi} \phi S=S \phi R_{\xi}$ holds on $M$, where $S$ denotes the Ricci tensor of type (1,1) on $M$.
%U http://arxiv.org/abs/0709.0436v1