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http://dx.doi.org/10.4134/BKMS.2011.48.6.1315

JACOBI OPERATORS ALONG THE STRUCTURE FLOW ON REAL HYPERSURFACES IN A NONFLAT COMPLEX SPACE FORM II  

Ki, U-Hang (Department of Mathematics Kyungpook National University)
Kurihara, Hiroyuki (Department of Liberal Arts and Engineering Sciences Hachinohe National College of Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.6, 2011 , pp. 1315-1327 More about this Journal
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;
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