Browse > Article
http://dx.doi.org/10.4134/CKMS.2012.27.2.327

A CLASSIFICATION OF (κ, μ)-CONTACT METRIC MANIFOLDS  

Yildiz, Ahmet (Art and Science Faculty Department of Mathematics Dumlupinar University)
De, Uday Chand (Department of Pure Mathematics University of Calcutta)
Publication Information
Communications of the Korean Mathematical Society / v.27, no.2, 2012 , pp. 327-339 More about this Journal
Abstract
In this paper we study $h$-projectively semisymmetric, ${\phi}$-pro-jectively semisymmetric, $h$-Weyl semisymmetric and ${\phi}$-Weyl semisym- metric non-Sasakian ($k$, ${\mu}$)-contact metric manifolds. In all the cases the manifold becomes an ${\eta}$-Einstein manifold. As a consequence of these results we obtain that if a 3-dimensional non-Sasakian ($k$, ${\mu}$)-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an N($k$)-contact metric manifold.
Keywords
semisymmetric spaces; ($k$, ${\mu}$)-contact metric manifolds; non-Sasakian manifolds; ${\eta}$-Einstein manifolds; $h$-projectively semisymmetric; ${\phi}$-projectively semisymmetric; $h$-Weyl semisymmetric; ${\phi}$-Weyl semisymmetric;
Citations & Related Records
연도 인용수 순위
  • Reference
1 B. J. Papantoniou, Contact Riemannian manifolds satifying R($\varepsilon$,X) ${\cdot}$ R = 0 and $\varepsilon$ $\in$ (k, $\mu$)-nullity distribution, Yokohama Math. J. 40 (1993), no. 2, 149-161.
2 Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X, Y ) ${\cdot}$ R = 0. I. The local version, J. Differential Geom. 17 (1982), no. 4, 531-582.
3 T. Takahashi, Sasakian $\phi$-symmetric spaces, Tohoku Math. J. (2) 29 (1977), no. 1, 91-113.   DOI
4 S. Tanno, Ricci Curvatures of contact Riemannian manifolds, Tohoku Math. J. (2) 40 (1988), no. 3, 441-448.   DOI
5 J. Vilms, Submanifolds of Euclidean space with parallel second fundamental form, Proc. Amer. Math. Soc. 32 (1972), 263-267.
6 K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies 32, Princeton University Press, 1953.
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 (k; $\mu$)-spaces, Illinois J. Math. 44 (2000), no. 1, 212-219.
9 U. C. De, A. A. Shaikh, and S. Biswas, On $\Phi$-recurrent Sasakian manifolds, Novi Sad J. Math. 33 (2003), no. 2, 43-48.
10 E. Boeckx, P. Buecken, and L. Vanhecke, $\phi$-symmetric contact metric spaces, Glasg. Math. J. 41 (1999), no. 3, 409-416.   DOI
11 O. Kowalski, An explicit classification of 3-dimensional Riemannian spaces satisfying R(X, Y ) ${\cdot}$ R = 0, Czechoslovak Math. J. 46(121) (1996), no. 3, 427-474.