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

  • Kim, Nam-Gil (Department of Mathematics, Chosun University) ;
  • Ki, U-Hang (Department of Mathematics, Kyungpook National University) ;
  • Kurihara, Hiroyuki (Department of Computer and Media Science, Saitama Junior College)
  • Received : 2008.07.07
  • Accepted : 2008.09.01
  • Published : 2008.09.25

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 ${\nabla}_{\xi}R_{\xi}=0$ characterize the homogeneous real hypersurfaces of type A in a complex: projective space $P_n{\mathbb{C}}$ or a complex hyperbolic space $H_n{\mathbb{C}}$ when $g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})$ 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

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Cited by

  1. CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A NONFLAT COMPLEX SPACE FORM WHOSE STRUCTURE JACOBI OPERATOR IS ξ-PARALLEL vol.31, pp.2, 2009, https://doi.org/10.5831/HMJ.2009.31.2.185