대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제48권6호
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  • Pages.1315-1327
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  • 2011
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2010.08.17
  • 발행 : 2011.11.30
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초록

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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참고문헌

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피인용 문헌

  1. REAL HYPERSURFACES OF NON-FLAT COMPLEX SPACE FORMS WITH GENERALIZED ξ-PARALLEL JACOBI STRUCTURE OPERATOR vol.58, pp.03, 2016, https://doi.org/10.1017/S0017089515000403