Bulletin of the Korean Mathematical Society (대한수학회보)

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JACOBI OPERATORS ALONG THE STRUCTURE FLOW ON REAL HYPERSURFACES IN A NONFLAT COMPLEX SPACE FORM II

  • Ki, U-Hang (Department of Mathematics Kyungpook National University) ;
  • Kurihara, Hiroyuki (Department of Liberal Arts and Engineering Sciences Hachinohe National College of Technology)
  • Received : 2010.08.17
  • Published : 2011.11.30
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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 ${\nabla}_{\xi}R_{\xi}=0$ characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when $R_{\xi}{\phi}S=R_{\xi}S{\phi}$ holds on M, where S denotes the Ricci tensor of type (1,1) on M.

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References

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