대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제45권4호
  • /
  • Pages.689-700
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  • 2008
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON Φ-RECURRENT (k, μ)-CONTACT METRIC MANIFOLDS

  • Jun, Jae-Bok (DEPARTMENT OF MATHEMATICS COLLEGE OF NATURAL SCIENCE KOOKMIN UNIVERSITY) ;
  • Yildiz, Ahmet (ART AND SCIENCE FACULTY DEPARTMENT OF MATHEMATICS DUMLUPINAR UNIVERSITY) ;
  • De, Uday Chand (DEPARTMENT OF MATHEMATICS UNIVERSITY OF KALYANI)
  • 발행 : 2008.11.30
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초록

In this paper we prove that a $\phi$-recurrent (k, $\mu$)-contact metric manifold is an $\eta$-Einstein manifold with constant coefficients. Next, we prove that a three-dimensional locally $\phi$-recurrent (k, $\mu$)-contact metric manifold is the space of constant curvature. The existence of $\phi$-recurrent (k, $\mu$)-manifold is proved by a non-trivial example.

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참고문헌

  1. C. Baikoussis, D. E. Blair, and T. Koufogiorgos, A decomposition of the curvature tensor of a contact manifold satisfying $R(X,Y)\xi=\kappa(\eta(Y)X-\eta(X)Y)$, Mathematics Technical Report, University of Ioannina, 1992
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  6. D. E. Blair, T. Koufogiorgos, and R. Sharma, A classification of 3-dimensional contact metric manifolds with $Q\phi = \phi{Q}$, Kodai Math. J. 13 (1990), no. 3, 391-401 https://doi.org/10.2996/kmj/1138039284
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  9. U. C. De and A. K. Gazi, On $\Phi$-recurrent N(k)-contact metric manifolds, Math. J. Okayama Univ. 50 (2008), 101-112
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  11. J.-B. Jun and U.-K. Kim, On 3-dimensional almost contact metric manifolds, Kyungpook Math. J. 34 (1994), no. 2, 293-301
  12. B. J. Papantoniou, Contact Riemannian manifolds satisfying R($\xi$,X)R = 0 and $\xi\, \in $ (k, )-nullity distribution, Yokohama Math. J. 40 (1993), no. 2, 149-161
  13. T. Takahashi, Sasakian ϕ-symmetric spaces, Tohoku Math. J. (2) 29 (1977), no. 1, 91-113 https://doi.org/10.2748/tmj/1178240699
  14. S. Tanno, Ricci curvatures of contact Riemannian manifolds, Tohoku Math. J. (2) 40 (1988), no. 3, 441-448 https://doi.org/10.2748/tmj/1178227985

피인용 문헌

  1. On ϕ-quasiconformally symmetric (κ,μ)-contact manifolds vol.31, pp.4, 2010, https://doi.org/10.1134/S1995080210040086
  2. CERTAIN SEMISYMMETRY PROPERTIES OF (𝜅, 𝜇)-CONTACT METRIC MANIFOLDS vol.53, pp.4, 2016, https://doi.org/10.4134/BKMS.b150638