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June 2009 Jacobi operators along the structure flow on real hypersurfaces in a nonflat complex space form
U-Hang Ki, Hiroyuki Kurihara, Ryoichi Takagi
Tsukuba J. Math. 33(1): 39-56 (June 2009). DOI: 10.21099/tkbjm/1251833206

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 $R_{\xi}\phi S=S\phi R_{\xi}$ holds on $M$, where $S$ denotes the Ricci tensor of type (1,1) on $M$.

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U-Hang Ki. Hiroyuki Kurihara. Ryoichi Takagi. "Jacobi operators along the structure flow on real hypersurfaces in a nonflat complex space form." Tsukuba J. Math. 33 (1) 39 - 56, June 2009. https://doi.org/10.21099/tkbjm/1251833206

Information

Published: June 2009
First available in Project Euclid: 1 September 2009

zbMATH: 1180.53021
MathSciNet: MR2553837
Digital Object Identifier: 10.21099/tkbjm/1251833206

Subjects:
Primary: 53B20, 53C15, 53C25

Rights: Copyright © 2009 University of Tsukuba, Institute of Mathematics

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Vol.33 • No. 1 • June 2009
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