DOI QR코드

DOI QR Code

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

  • Kim, Nam-Gil (Department of Mathematics Chosun University)
  • Received : 2009.05.20
  • Accepted : 2009.06.02
  • Published : 2009.06.25

Abstract

Let M be a real hypersurface with almost contact metric structure $({\phi},{\xi},{\eta},g)$ of a nonflat complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},{\xi}){\xi}$ is ${\xi}$-parallel. In this paper, 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.

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