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

Soo Jin Kim|U-Hang Ki|Hiroyuki Kurihara
경북대학교 자연과학대학 수학과|2016.06|Kyungpook Mathematical Journal|제56권 제2호|pp. 541-575

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참고문헌

키워드

complex space formstructure Jacobi operatorreal hypersurfacestructure tensorRicci tensor.
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초록

Let $M$ be a real hypersurface of a complex space form with almostcontact metric structure $(\phi, \xi, \eta, g)$. In this paper, weprove that if the structure Jacobi operator $R_\xi=R(\cdot,\xi)\xi$ is$\phi\nabla_{\xi} \xi$-parallel and $R_{\xi}$ commute with thestructure tensor $\phi$, then $M$ is a homogeneous real hypersurface ofType A provided that Tr$R_{\xi}$ is constant.

Abstract

Let $M$ be a real hypersurface of a complex space form with almostcontact metric structure $(\phi, \xi, \eta, g)$. In this paper, weprove that if the structure Jacobi operator $R_\xi=R(\cdot,\xi)\xi$ is$\phi\nabla_{\xi} \xi$-parallel and $R_{\xi}$ commute with thestructure tensor $\phi$, then $M$ is a homogeneous real hypersurface ofType A provided that Tr$R_{\xi}$ is constant.

참고문헌 (18)

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