Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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NOTE ON REAL HYPERSURFACES OF NONFLAT COMPLEX SPACE FORMS IN TERMS OF THE STRUCTURE JACOBI OPERATOR AND RICCI TENSOR

  • KIM, NAM-GIL (Department of Mathematics Chosun University) ;
  • LI, CHUNJI (Institute of System Science College of Sciences, Northeastern University) ;
  • KI, U-HANG (Department of Mathematics Kyungpook National University)
  • Received : 2005.04.21
  • Published : 2005.09.25
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Abstract

Let M be a real hypersurface with almost contact metric structure (${\phi}$, ${\xi}$, ${\eta}$, g) in a nonflat complex space form $M_n(c)$. We denote by A and S be the shape operator and the Ricci tensor of M respectively. In the present paper we investigate real hypersurfaces with $g(SA{\xi},\;A{\xi})=const$. of $M_n(c)$ whose structure Jacobi operator $R_{\xi}$ commute with both ${\phi}$ and S. We give a characterization of Hopf hypersurfaces of $M_n(c)$.

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References

  1. J. Reine Angew. Math. v.395 Real hypersurfaces with constant principal curvatures in a complex hyperbolic space Berndt, J.
  2. Acta. Math. Hungar. v.80 Real hypersurfaces of a complex projective space in terms of the Jacobi operators Cho, J.T.;Ki, U.H.
  3. Comm. Korean Math. Soc. v.13 The Jacobi operator of real hypersurfaces of a complex space form Ki, U.H.;Kim, H.J.;Lee, A.A.
  4. Bull. Korean Math. Soc. v.42 The structure Jacobi operator on real hyper-surfaces in a nonflat complex space form Ki, U.H.;Kim, S.J.;Lee, S.B.
  5. Real hypersurfaces in nonflat complex forms concerned with the structure Jacobi operator and Ricci tensor;Topics in Almost Hermitian Geometry and Related Fields Ki, U.H.;Nagai, S.;Takagi, R.
  6. Math. J. Okayama Univ. v.32 On real hypersurfaces of a complex space form Ki, U.H.;Suh, Y.J.
  7. Trans. Amer. Soc. v.296 Real hypersurfaces and complex submanifolds in complex projective space Kimura, M.
  8. Real hypersurfaces in complex space forms;Tight and Taut submanifolds Niebergall, R.;Ryan, P.J.;Cecil, T.E.(ed.);Chern, S.S.(ed.)
  9. Osaka J. Math. v.10 On homogeneous real hypersurfaces in a complex projective space Takagi, R.