CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM USED BY THE ζ-PARALLEL STRUCTURE JACOBI OPERATOR

• Journal title : Honam Mathematical Journal
• Volume 30, Issue 3,  2008, pp.535-550
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2008.30.3.535
Title & Authors
CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM USED BY THE ζ-PARALLEL STRUCTURE JACOBI OPERATOR
Kim, Nam-Gil; Ki, U-Hang; Kurihara, Hiroyuki;

Abstract
Let M be a real hypersurface of a complex space form with almost contact metric structure $\small{({\phi},{\xi},{\eta},g)}$. In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $\small{R_{\xi}=R({\cdot},{\xi}){\xi}}$ is $\small{{\xi}}$-parallel. In particular, we prove that the condition $\small{{\nabla}_{\xi}R_{\xi}=0}$ characterize the homogeneous real hypersurfaces of type A in a complex: projective space $\small{P_n{\mathbb{C}}}$ or a complex hyperbolic space $\small{H_n{\mathbb{C}}}$ when $\small{g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})}$ is constant and not equal to -c/24 on M, where c is a constant holomorphic sectional curvature of a complex space form.
Keywords
complex;space form;real hypersurface;structure Jacobi operator;
Language
English
Cited by
1.
CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A NONFLAT COMPLEX SPACE FORM WHOSE STRUCTURE JACOBI OPERATOR IS ξ-PARALLEL, Honam Mathematical Journal, 2009, 31, 2, 185
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