CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A NONFLAT COMPLEX SPACE FORM WHOSE STRUCTURE JACOBI OPERATOR IS ξ-PARALLEL

• Journal title : Honam Mathematical Journal
• Volume 31, Issue 2,  2009, pp.185-201
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2009.31.2.185
Title & Authors
CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A NONFLAT COMPLEX SPACE FORM WHOSE STRUCTURE JACOBI OPERATOR IS ξ-PARALLEL
Kim, Nam-Gil;

Abstract
Let M be a real hypersurface with almost contact metric structure $\small{({\phi},{\xi},{\eta},g)}$ of a nonflat complex space form whose structure Jacobi operator $\small{R_{\xi}=R({\cdot},{\xi}){\xi}}$ is $\small{{\xi}}$-parallel. In this paper, 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.
Keywords
real hypersurface;structure Jacobi operator;Ricci tensor;Hopf hypersurface;
Language
English
Cited by
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