ON LORENTZIAN TRANS-SASAKIAN MANIFOLDS

Year 2013, Volume: 62 Issue: 2, 37 - 51, 01.08.2013

U.c. De Krishnendu De

https://doi.org/10.1501/Commua1_0000000697

Cited By: 2

Abstract

The object of the present paper is to study the Trans-Sasakianstructure on a manifold with Lorentzian metric. Several interesting results areobtained on the manifold. Also conformally *at Lorentzian Trans-Sasakianmanifolds have been studied. Next, in three- dimensional Lorentzian TransSasakian manifolds, explicit formulae for Ricci operator, Ricci tensor andcurvature tensor are obtained.Lorentzian Trans-Sasakian manifold of type ( ; ) is locallyand only if the scalar curvature r is constant providedFinally, we give some examples of three-dimensional Lorentzian Trans-Sasakianmanifold

Keywords

Lorentzian Trans-Sasakian manifold , -Einstein manifold, conformally *at manifold, locally-symmetric manifold

References

• Blair, D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Math., Springer Verlag, (509)1976.
• Blair, D. E.and Oubina, J.A., Conformal and related changes of metric on the product of two almost contact metric manifolds, Publ. Mat.34(1)(1990), 199
• De, U.C.and Tripathi,M.M., Ricci tensor in 3-dimensional trans-Sasakian manifolds, Kyungpook Math.J.43(2)(2003),247
• Janssen, D. and Vanhecke, L., Almost contact structures and curvature tensors, Kodai Math. J.,4(1981),1
• Gill, H. and Dube, K.K., Generalized CR- Submanifolds of a trans Lorentzian para Sasakian manifold, Proc. Nat. Acad. Sci. India Sec. A Phys. 2(2006), 119
• Gray, A. and Hervella, L.M., The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Math. Pura Appl., (4) 123 (1980), 35
• Ikawa, T. and Erdogan, M., Sasakian manifolds with Lorentzian metric, Kyungpook Math. J. 35(1996), 517
• Marrero, J.C., The local structure of trans-sasakian manifolds, Ann.Mat.Pura Appl.(4)162 (1992),77-86.
• Matsumoto, K., On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Nat. Science, (1989), 151
• Matsumoto,K. and Mihai,I., On a certain transformation in a Lorentzian Para-Sasakian Manifold, Tensor (N.S.), 47(1988), 189
• Matsumoto, K. , Mihai,I. and Rosca, R., -null geodesic gradient vector …elds on a Lorentzian para-Sasakian manifold. J. Korean Math. Soc. 32(1995), 17
• Mihai, I., Oiaga, A. and Rosca, R., Lorentzian Kenmotsu manifolds having two skew- sym- metric conformal vector …elds, Bull. Math. Soc. Sci. Math. Roumania, 42(1999), 237
• Mihai,I. and Rosca, R., On Lorentzian P-Sasakian Manifolds, Classical Analysis. World Scienti…c, Singapore, 1992 155
• Oubina, J.A., New classes of almost contact metric structures, Publicationes Mathematicae Debrecen 32 (1985), 21
• Shaikh, A. A., Baishya, K. K. and Eyasmin, S., On D-homothetic deformation of trans- sasakian structure, Demonstratio Mathematica, 1 2008, 171
• Takahashi, T., Sasakian symmetric spaces, Tohoku Math.J.(2)29, (1)(1977),91-113.
• Yaliniz, A.F., Yildiz, A. and Turan, M., On three-dimensional Lorentzian Kenmotsu manifolds, Kuwait J. Sci. Eng. 36 (2009), 51
• Yildiz, A., Turan, M. and Murathan, C., A class of Lorentzian Sasakian manifolds, Kyungpook Math. J. 49(2009), 789
• Current address : Uday Chand De,, Department of Pure Mathematics,, Calcutta University ,, Kol , Krishnendu De, Konnagar High School(H.S.),, 68 G.T. Road (West),Konnagar,Hooghly, Pin.712235, West Bengal, INDIA. Road, ,West Bengal, INDIA.
• E-mail address : [e-mail], [e-mail] URL: http://communications.science.ankara.edu.tr/index.php?series=A1