Browse > Article
http://dx.doi.org/10.4134/BKMS.2008.45.4.689

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.4, 2008 , pp. 689-700 More about this Journal
Abstract
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.
Keywords
(k, $\mu$)-contact metric manifolds; $\eta$-Einstein manifold; $\phi$-recurrent (k, $\mu$)-contact metric manifolds;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
1 U. C. De, A. A. Shaikh, and S. Biswas, On $\Phi$-recurrent Sasakian manifolds, Novi Sad J. Math. 33 (2003), no. 2, 43-48
2 J.-B. Jun and U.-K. Kim, On 3-dimensional almost contact metric manifolds, Kyungpook Math. J. 34 (1994), no. 2, 293-301
3 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
4 T. Takahashi, Sasakian ϕ-symmetric spaces, Tohoku Math. J. (2) 29 (1977), no. 1, 91-113   DOI
5 D. E. Blair, J. S. Kim, and M. M. Tripathi, On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc. 42 (2005), no. 5, 883-892   과학기술학회마을   DOI   ScienceOn
6 U. C. De and A. K. Gazi, On $\Phi$-recurrent N(k)-contact metric manifolds, Math. J. Okayama Univ. 50 (2008), 101-112
7 D. E. Blair, T. Koufogiorgos, and B. J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math. 91 (1995), no. 1-3, 189-214   DOI
8 E. Boeckx, A full classification of contact metric ($\kappa,\,\mu$)-spaces, Illinois J. Math. 44 (2000), no. 1, 212-219
9 E. Boeckx, P. Buecken, and L. Vanhecke, $\phi$-symmetric contact metric spaces, Glasg. Math. J. 41 (1999), no. 3, 409-416   DOI
10 S. Tanno, Ricci curvatures of contact Riemannian manifolds, Tohoku Math. J. (2) 40 (1988), no. 3, 441-448   DOI
11 D. E. Blair and H. Chen, A classification of 3-dimensional contact metric manifolds with $Q\phi = \phi{Q}$. II, Bull. Inst. Math. Acad. Sinica 20 (1992), no. 4, 379-383
12 D. E. Blair, Two remarks on contact metric structures, Tohoku Math. J. (2) 29 (1977), no. 3, 319-324   DOI
13 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   DOI
14 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