Browse > Article
http://dx.doi.org/10.4134/BKMS.b150638

CERTAIN SEMISYMMETRY PROPERTIES OF (𝜅, 𝜇)-CONTACT METRIC MANIFOLDS  

De, Uday Chand (Department of Pure Mathematics Calcutta University)
Jun, Jae-Bok (Department of Mathematics College of Natural Science)
Samui, Srimayee (Umeschandra college)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.4, 2016 , pp. 1237-1247 More about this Journal
Abstract
The object of the present paper is to characterize $({\kappa}$, ${\mu}$)-contact metric manifolds whose concircular curvature tensor satisfies certain semisymmetry conditions. We also verify that the result holds by a concrete example.
Keywords
(${\kappa}$, ${\mu}$)-contact metric manifolds; $N({\kappa})$-contact metric manifolds; concircular curvature tensor; ${\eta}$-Einstein manifolds;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 K. Arslan, R. Ezentas, C. Murathan, and T. Sasahara, Biharmonic submanifolds in 3-dimensional ($\mathit{k},\mu$)-manifolds, Int. J. Math. Math. Sci. 2005 (2005), no. 22, 3575-3586.   DOI
2 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.   DOI
3 D. E. Blair, T. Koufogiorgos, and B. J. Papantoniou, Contact metric manifold satisfying a nullity condition, Israel J. Math. 91 (1995), no. 1-3, 189-214.   DOI
4 U. C. De and A. Sarkar, On quasi-conformal curvature tensor of ($\mathit{k},\mu$)-contact metric manifold, Math. Rep. (Bucur.) 14(64) (2012), no. 2, 115-129.
5 S. Ghosh and U. C. De, On $\phi$-quasiconformally symmetric ($\mathit{k},\mu$)-contact metric manifolds, Lobachevskii J. Math. 31 (2010), no. 4, 367-375.   DOI
6 S. Ghosh and U. C. De, On a class of ($\mathit{k},\mu$)-contact metric manifolds, An. Univ. Oradea Fasc. Mat. 19 (2012), no. 1, 231-242.
7 J. B. Jun, A. Yildiz, and U. C. De, On $\phi$-recurrent ($\mathit{k},\mu$)-contact metric manifolds, Bull. Korean Math. Soc. 45 (2008), no. 4, 689-700.   DOI
8 W. Kuhnel, Conformal transformations between Einstein spaces, Conformal geometry (Bonn, 1985/1986), 105-146, Asepects math., E12, Vieweg, Braunschweig, 1988.
9 C. Ozgur, Contact metric manifolds with cyclic-parallel Ricci tensor, Differ. Geom. Dyn. Syst. 4 (2002), no. 1, 21-25.
10 B. J. Papantoniou, Contact Remannian manifolds satisfying $R(\xi,X){\cdot}R\;=\;0\;and\;\xi\;{\in}\;(\mathit{k},\mu)$-nullity distribution, Yokohama Math. J. 40 (1993), no. 2, 149-161.
11 S. Tanno, Ricci curvatures of contact Reimannian manifolds, Tohoku Math. J. 40 (1988), no. 3, 441-448.   DOI
12 K. Yano, Concircular geometry I. Concircular transformations, Proc. Imp. Acad. Tokyo 16 (1940), 195-200.   DOI
13 A. Yildiz and U. C. De, A classification of ($\mathit{k},\mu$)-contact metric manifolds, Comm. Korean Math. Soc. 27 (2012), no. 2, 327-339.   DOI