Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지

ON CHARACTERIZATIONS OF REAL HYPERSURFACES IN A COMPLEX SPACE FORM IN TERMS OF THE JACOBI OPERATORS

  • AHN, SEONG SOO (Department of Computer Dongshin University) ;
  • KIM, JONG CHUL (Education of Mathmatic Hankuk University of Foreign Studies Graduate School)
  • Received : 2004.02.19
  • Published : 2004.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

The shape operator or second fundamental tensor of a real hypersurface in $M_n(c)$ will be denoted by A, and the induced almost contact metric structure of the real hypersurface by (${\phi}$, <, >,${\xi}$, ${\eta}$). The purpose of this paper is to prove that is no ruled real hypersurface M in a complex space form $M_n(c)$, $c{\neq}0$, $n{\geq}3$, who satisfies $R_{\xi}{\phi}={\phi}R_{\xi}$ on M.

Keywords

References

  1. Tsukuba J. Math. v.17 On ruled real hypersurfaces in a complex space form Ahn, S.S.;Lee, S.B.;Suh, Y.J.
  2. J. Reine Angew Math. v.359 Real hypersurfaces with constant principal curvatures in a complex hyperbolic space Berndt, J.
  3. Math. Z. v.202 On real hypersurfaces of a complex projective space Kimura, M.;Maeda,S.
  4. Math. J. Okayama Univ. v.40 On real hypersurfaces in a complex space form Kurihara, H.
  5. Geometriae Dedicata v.20 On some real hypersurfaces of a complex hyperbolic space Montiel, S.;Romero, A.
  6. Real hypersurfaces in complex space forms;Tight and Taut Submanifolds Niebergall, R.;Ryan, P.J.;Cecil, T.E.(ed.)(et al.)
  7. Trans. Amer. Math. Soc. v.212 On some real hypersurfaces of a complex projective space Okumura, M.
  8. Curvature properties of real hypersurfaces in a complex space form Sohn, W.H.
  9. Osaka J. Math. v.10 On homogeneous real hypersurfaces of a complex projective space Takagi, R.
  10. Tohoku Math. J. v.50 The rigidity for real hypersurfaces in a complex projective space Takagi, R.;Kim, I.B.;Kim, B.H.