On δ- Lorentzian trans Sasakian manifold with semi-symmetric metric connection

Mohd Danish Siddiqi

doi:10.5269/bspm.41108

Mohd Danish Siddiqi Jazan University

Résumé

The aim of the present research is to study the δ-Lorentzian trans Sasakian manifolds with a semi-symmetric metric connection. We have found the expressions for curvature tensors, Ricci curvature tensors and scalar curvature of the δ-Lorentzian trans Sasakian manifolds with a semi-symmetric metric and metric connection. Also, we have discussed some results on quasi-projectively flat and ϕ-projectively flat manifolds endowed with a semi-symmetric-metric connection. It shown that the manifold satisfying
¯
R. ¯ S = 0,
¯
P, ¯ S = 0.
Lastly, we have obtained the conditions for the δ-Lorentzian Trans Sasakian manifolds with a semi-symmetric metric connection to be conformally flat and ξ-conformally flat.

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Biographie de l'auteur

Mohd Danish Siddiqi, Jazan University

Deparment of Mathematics

Assistant Professor

Références

Bagewadi, C. S. and Gatti, N. B., On irrotational quasi-conformal curvature tensor. Tensor.N.S., 64, 284-258, (2003).

Bagewadi, C. S., and Kumar, E. G., Note on Trans-Sasakian Manifolds. Tensor. N. S., 65, 80-88 (2004).

Bagewadi, C. S., and Venkatesha, Some Curvature Tensors on a Trans-Sasakian Manifold, Turk. J. Math. 31 (2007), 111-121.

Bhati, S. M., On weakly Ricci φ-symmetric δ-Lorentzian trans Sasakian manifolds, Bull. Math. Anal. Appl., vol. 5, (1), (2013), 36-43.

Bartolotti, E., Sulla geometria della variata a connection affine. Ann. di Mat. 4(8) (1930), 53-101.

Bejancu A. and Duggal K. L., Real hypersurfaces of indefinite Kaehler manifolds, Int. J. Math. Math. Sci. 16(1993), no. 3, 545-556.

Blair, D. E., Contact manifolds in Riemannian geometry, Lecture note in Mathematics, 509, Springer-Verlag Berlin-New York, 1976.

De, U. C and Shaikh, A. A., K-contact and Sasakian manifolds with conservative quasi-conformal curvature tensor. Bull. Cal. Math. Soc., 89, 349-354, (1997).

De, U. C. and Sarkar, A., On ǫ-Kenmotsu manifold, Hardonic J. 32 (2009), no.2, 231-242.

Friedmann, A. and Schouten, J. A., Uber die Geometric der halbsymmetrischen Ubertragung, Math. Z. 21 (1924), 211-223.

Gray, A. and Harvella, L. M., The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl., 123(4) (1980), 35-58.

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), 119-124.

Hayden, H. A., Subspaces of space with torsion, Proc. London Math. Soc. 34 (1932), 27-50.

Hirica, I. E. and Nicolescu, L., Conformal connections on Lyra manifolds, Balkan J. Geom. Appl., 13 (2008), 43-49.

Ikawa, T. and Erdogan, M., Sasakian manifolds with Lorentzian metric, Kyungpook Math. J. 35(1996), 517-526.

Jun, J. B., De, U. C. and Pathak, G., On Kenmotsu manifolds, J. Korean Math. Soc. 42 (2005), no. 3, 435-445.

Marrero, J. C., The local structure of Trans-Sasakian manifolds, Annali di Mat. Pura ed Appl. 162 (1992), 77-86.

Matsumoto, K., On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Nat. Science, 2(1989), 151-156.

Oubina, J. A., New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), 187-193

Pathak, G. and De, U. C., On a semi-symmetric connection in a Kenmotsu manifold, Bull. Calcutta Math. Soc. 94 (2002), no. 4, 319-324.

Pujar, S. S., and Khairnar, V. J., On Lorentzian trans-Sasakian manifold-I, Int. J. of Ultra Sciences of Physical Sciences, 23(1)(2011), 53-66.

Pujar, S. S., On Lorentzian Sasakian manifolds, to appear in Antactica J. of Mathematics 8(2012).

Sharfuddin, A. and Hussain, S. I., Semi-symmetric metric connections in almost contact manifolds, Tensor (N.S.), 30(1976), 133-139.

Shukla, S. S. and Singh, D. D., On (ǫ)-Trans-Sasakian manifolds, Int. J. Math. Anal. 49(4) (2010), 2401-2414.

Siddiqi, M. D, Haseeb, A. and Ahmad, M., A Note On Generalized Ricci-Recurrent (ǫ, δ)-Trans-Sasakian Manifolds, Palestine J. Math., Vol. 4(1), 156-163 (2015)

Tripathi, M. M., On a semi-symmetric metric connection in a Kenmotsu manifold, J. Pure Math. 16(1999), 67-71.

Tripathi, M. M., Kilic, E., Perktas S. Y. and Keles, S., Indefinite almost para-contact metric manifolds, Int. J. Math. and Math. Sci. (2010), art. id 846195, pp. 19.

Takahashi, T., Sasakian manifolds with Pseudo -Riemannian metric, Tohoku Math.J. 21 (1969),271-290.

Tanno, S., The automorphism groups of almost contact Riemannian manifolds, Tohoku Math.J. 21 (1969),21-38.

Xufeng, X. and Xiaoli, C., Two theorem on ǫ-Sasakian manifolds, Int. J. Math. Math. Sci. 21 (1998), no. 2, 249-54.

Yaliniz, A.F., Yildiz, A. and Turan, M., On three-dimensional Lorentzian β- Kenmotsu manifolds, Kuwait J. Sci. Eng. 36 (2009), 51-62.

Yildiz, A., Turan, M. and Murathan, C., A class of Lorentzian α- Sasakian manifolds, Kyung-pook Math. J. 49(2009), 789 -799.

Yano, K., On semi-symmetric metric connections, Revue Roumaine De Math. Pures Appl. 15(1970), 1579-1586.