- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Jacobi operators along the structure flow on real hypersurfaces in a nonflat complex space form II Bull. Korean Math. Soc. 2011 Vol. 48, No. 6, 1315-1327 https://doi.org/10.4134/BKMS.2011.48.6.1315Printed November 1, 2011 U-Hang Ki and Hiroyuki Kurihara Kyungpook National University, Hachinohe National College of Technology Abstract : 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 $R_{\xi}\phi S=R_{\xi} S\phi$ holds on $M$, where $S$ denotes the Ricci tensor of type (1,1) on $M$. Keywords : complex space form, real hypersurface, structure Jacobi operator, Ricci tensor MSC numbers : Primary 53B20, 53C15, 53C25 Downloads: Full-text PDF