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http://dx.doi.org/10.5666/KMJ.2016.56.2.541

Jacobi Operators with Respect to the Reeb Vector Fields on Real Hypersurfaces in a Nonflat Complex Space Form  

Ki, U-Hang (The National Academy of Siences)
Kim, Soo Jin (Department of Mathematics Chosun University)
Kurihara, Hiroyuki (The College of Education, Ibaraki University)
Publication Information
Kyungpook Mathematical Journal / v.56, no.2, 2016 , pp. 541-575 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 prove that if the structure Jacobi operator $R_{\xi}= R({\cdot},{\xi}){\xi}$ is ${\phi}{\nabla}_{\xi}{\xi}$-parallel and $R_{\xi}$ commute with the structure tensor ${\phi}$, then M is a homogeneous real hypersurface of Type A provided that $TrR_{\xi}$ is constant.
Keywords
complex space form; real hypersurface; structure Jacobi operator; structure tensor; Ricci tensor;
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Times Cited By KSCI : 1  (Citation Analysis)
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