Jacobi operators along the structure flow on real hypersurfaces in a nonflat complex space form

Ki, U-Hang; Kurihara, Hiroyuki; Takagi, Ryoichi

Jacobi operators along the structure flow on real hypersurfaces in a nonflat complex space form

Authors

Ki, U-Hang

Kurihara, Hiroyuki

Takagi, Ryoichi

Description

Let $M$ be a real hypersurface of a complex space form with almost contact metric structure $(ϕ, ξ, η, g)$. In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_ξ=R(\cdot,ξ)ξ$ is $ξ$-parallel. In particular, we prove that the condition $\nabla_ξ R_ξ=0$ characterizes the homogeneous real hypersurfaces of type $A$ in a complex projective space or a complex hyperbolic space when $R_ξ ϕS=S ϕR_ξ$ holds on $M$, where $S$ denotes the Ricci tensor of type (1,1) on $M$.
14 pages