Concircular Vectors Field in (kappa; mu)-Contact Metric Manifolds

Yıl 2018, Cilt: 11 Sayı: 1, 52 - 56, 30.04.2018

Pradip Majhi Gopal Ghosh

Öz

The aim of the present paper is to study (kappa,mu)-contact manifolds admitting a non-null concircular

vector field and concurrent vector field. We prove that in both the cases the manifold becomes a

Sasakian manifold under certain restriction on kappa, mu.

Anahtar Kelimeler

(kappa; mu) contact manifolds, Concircular vector field, Concurrent vector field

Kaynakça

• [1] Blair, D. E., Koufogiorgos, T., Papantoniou, B. J., Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91(1995), 189-214.
• [2] Blair, D. E., Contact manifolds in Riemannian geomatry , Lecture notes in math., springer-verlag, 509(1976).
• [3] Blair, D. E., Riemannian geomatry of contact and Sympletic Manifolds , Progress in Math. , Birkhuser, Boston, 203(2002).
• [4] Boeckx, E., A full clasification of contact metric (kappa,mu)- spaces, Illinois J. Math., 44(2000), 212-219.
• [5] Bagewadi, C. S., Venkatesha., Torseforming vector field in a Tran-Sasakian manifold, Differential Geometry-Dynamical System, 8(2006), 23-28.
• [6] De, U. C., Kim, Y. H., Shaikh, A. A., Contact metric manifolds with  belong to the (k; )-nullity distribution, Indian J. Math., 47(2005), 295-304.
• [7] De, U. C., Pathak, G., Torseforming vector field in a Kenmotsu manifold, Analele Stintifice Ale Universitatii "AL. I. CUZA", XLIX(2003), 257-264.
• [8] De, U. C., Ghosh, S., On quasi-conformal curvature tensor of (kappa,mu)-contact manifolds, Lobachevskii J. Math. 31(2010), 367-375.
• [9] De, U. C., Sarkar, A., On quasi-conformal curvature tensor of (kappa,mu)-contact manifolds, Math. Rep. (Bucur), 64(2012), 115-129.
• [10] De, U. C., Jun, J. B., Samui, S., Certain semisymmetry properties of (kappa,mu)-contact manifolds, Bull.Korean. Math. Soc. 53(2012), 1237-1247.
• [11] Ghosh, S., De, U. C., On a class of (kappa,mu)-contact manifolds, Analele universitattii oradea, Fasc. Mathematica, XIX(2012), 231-242.
• [12] Papantoniou, B. J., Contact manifolds,harmonic curvature tensor and (kappa,mu)-nullity distribution, Comment Math. Univ. Carolinne, 34(1993), 323-334.
• [13] Shirokov, P. A., Collected works of geometry, Kazan Univ. Press, (1966).
• [14] Tanno, T., The topology of contact Riemannian-manifolds, Illinois J. Math., 12 (1968), 700-717.
• [15] Yildiz, A., De, U. C., A classification of (kappa,mu)-contact manifolds, Commun. Korean Math. Soc.,27(2012), 327-339.
• [16] Yildiz, A., Jun, J. B., De, U. C., On phi recurrent (kappa,mu)-contact manifolds, Bull. Korean Math. Soc., 45(2008), 689-700.
• [17] Yildiz, A., Murathan, C., Contact Riemannian manifolds satisfying C(;X)
  S = 0 and  2 (kappa,mu)-nullity distribution, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 49(2000), 33-37.
• [18] Yano, K., On the torseforming direction in Riemannian spaces, Proc. Imp. Acad. Tokyo, 20(1994), 340-345.