Some classes of 3-dimensional Trans-Sasakian manifolds with respect to semi-symmetric metric connection

Sampa Pahan

doi:10.5269/bspm.42855

Authors

Sampa Pahan University of Kalyani

DOI:

https://doi.org/10.5269/bspm.42855

Abstract

The object of the present paper is to study semi-symmetric metric connection on a 3-dimensional trans-Sasakian manifold. We found the necessary condition under which a vector field on a 3-dimensional trans-Sasakian manifold will be a strict contact vector field. Then, we obtained extended generalized phi-recurrent 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection. Next, a 3-dimensional trans-Sasakian manifold satises the condition ~L.~ S = 0 with respect to semi-symmetric metric connection is studied.

References

1. Amur, K. and Pujar, S. S., On submanifolds of a Riemannian manifold admitting a metric semi-symmetric connection, Tensor, N.S., 32, 35-38, (1978).
2. Basari, A. and Murathan, C., On generalized Ï†-recurrent kenmotsu manifolds, Sdu Fen Edebiyat Fakultesi Fen Dergisi (E-DERGI), 10 , 91-97, (2008).
3. Bagewadi, C. S., On totally real submanifolds of a Ka¨hlerian manifold admitting semi-symmetric F-connection, Indian J. Pure. Appl. Math., 13, 528-536, (1982).
4. Friedmann, A. and Schouten, J. A., U¨ber die Geometrie der halbsymmetrischen Ubertragungen, Math.Z., 21, 211-223, (1924). https://doi.org/10.1007/BF01187468
5. Hayden, H. A., Subspace of a space with torsion, Proceedings of the London Mathematical Society II Series, 34 , 27-50, (1932). https://doi.org/10.1112/plms/s2-34.1.27
6. Marrero, J. C., The local structure of trans-Sasakian manifolds, Ann. Mat. Pura. Appl., 162(4), 77-86. (1992). https://doi.org/10.1007/BF01760000
7. Prakasha, D. G., On extended generalized Ï†-recurrent Sasakian manifolds, J. Egyptian Math. Soc., 21(1), 25-31, (2013). https://doi.org/10.1016/j.joems.2012.11.002
8. Prakasha, D. G., Bagewadi, C. S. and Venkatesha, Conformaly and quasi-conformally conservative curvature tensor on a trans-sasakian manifolds with respect to semi-symmetric metric connection, Diff. Geometry-Dyn. Sys., 10, 263-274, (2007).
9. Prasad , R. and Srivastava, V., Some results on trans-Sasakian manifold, Matematicki Vesnik, 65(3), 346-352, (2013).
10. Osserman, R., Curvature in the Eighties, The American mathematical monthly 97 (8), 731-756, (1990). https://doi.org/10.1080/00029890.1990.11995659
11. Oubina, J. A., New classes of almost contact metric structures, pub. Math. Debrecen, 32, 187-193, (1985).
12. Ozgur, C., On Ï†âˆ’conformally flat Lorentzian para-Sasakian manifolds, Radovi Matematicki, 12, 99-106, (2003).
13. Schouten, J. A., Ricci-Calculus-An Introduction to Tensor Analysis and Geometrical Applications, Springer-Verlag, Berlin-G¨ottingen-Heidelberg, 1954.
14. Siddiqui, S. A. and Ahsan, Z., Conharmonic curvature tensor and space-time of general relativity, Diff. Geometry-Dyn. Syst., 12, 213-220, (2010).
15. Sharafuddin, A. and Hussain, S. I., Semi-symmetric metric connections in almost contact manifolds, Tensor, N.S., 30, 133-139, (1976).
16. Shaikh, A. A. and Hui, S. K., On extended generalized Ï†-recurrent Î²-Kenmotsu manifolds, Publications De L'Institut Math'ematique Nouvelle s'erie, tome, 89(103), 77-88, (2011). https://doi.org/10.2298/PIM1103077A
17. Tarafdar, M. and Bhattacharyya, A., A special type of trans-Sasakian manifolds, Tensor (N.S.), 64(3), 274-281, (2003).
18. Yano, K., On semi-symmetric metric connection, Revue Roumaine Math. Pures App., 15, 1579-1586, (1970).