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

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

2007-09-04

arxiv.org/abs/0709.0436v1

Mathematics

Differential Geometry

14 pages

Scientific paper

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 $M$.

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