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Structure Jacobi Operators of Real Hypersurfaces with Constant Mean Curvature in a Complex Space Form

U-Hang Ki|Hiroyuki Kurihara|Tae Yong Hwang
경북대학교 자연과학대학 수학과|2016.12|Kyungpook Mathematical Journal|제56권 제4호|pp. 1207-1235

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키워드

structurecomplex space formreal hypersurface
주제분류수학

초록

Let $M$ be a real hypersurface with constant mean curvature in a complex space form $M_n (c), c\ne 0$. In this paper, we prove that if the structure Jacobi operator $R_\xi=R(\cdot,\xi)\xi$ with respect to the structure vector field $\xi$ is $\phi\nabla_{\xi} \xi$-parallel and $R_{\xi}$ commute with the structure tensor field $\phi$, then $M$ is a homogeneous real hypersurface of Type A.

Abstract

Let $M$ be a real hypersurface with constant mean curvature in a complex space form $M_n (c), c\ne 0$. In this paper, we prove that if the structure Jacobi operator $R_\xi=R(\cdot,\xi)\xi$ with respect to the structure vector field $\xi$ is $\phi\nabla_{\xi} \xi$-parallel and $R_{\xi}$ commute with the structure tensor field $\phi$, then $M$ is a homogeneous real hypersurface of Type A.

참고문헌 (16)

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관련 논문AI추천

Jacobi Operators with Respect to the Reeb Vector Fields on Real Hypersurfaces in a Non at Complex Space FormHiroyuki Kurihara, Soo Jin Kim, U-Hang Ki경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호Structure Jacobi Operators and Real Hypersurfaces of Type(A) in Complex Space Forms기우항영남수학회 · East Asian Mathematical Journal2021 · 제37권 제1호Jacobi operators along the structure flow on real hypersurfaces in a nonflat complex space form II기우항, Hiroyuki Kurihara대한수학회 · 대한수학회보2011 · 제48권 제6호Real Hypersurfaces in a Nonflat Complex Space Form with Special Structure Tensor Field김훈주, 임동호한국수학교육학회 · 이론수학과 교직수학2021 · 제28권 제3호Certain Characterization of Real Hypersurfaces of type A in a Nonflat Complex Space Form기우항경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2021 · 제61권 제1호CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM기우항, 김인배, 임동호대한수학회 · 대한수학회보2010 · 제47권 제1호

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