Lorentzian para-Sasakian Manifolds Admitting a New Type of Quarter-symmetric Non-metric -connection
Lorentzian para-Sasakian Manifolds Admitting a New Type of Quarter-symmetric Non-metric -connection
We define a new type of quarter-symmetric non-metric -connection on an LP-Sasakian manifoldand prove its existence. We provide its application in the general theory of relativity. To validatethe existence of the quarter-symmetric non-metric -connection on an LP-Sasakian manifold, wegive a non-trivial example in dimension 4 and verify our results.
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- [1] Arslan, K., Deszcz, R., Ezentas, R., Hotlos, M. and Murathan, C., On generalized Robertson-Walker spacetimes satisfying some curvature
condition. Turk J Math 38 (2014), 353-373.
- [2] Aqeel, A. A., De, U. C. and Ghosh, G. C., On Lorentzian para-Sasakian manifolds. Kuwait J. Sci. Eng. 31 (2004), no. 2, 1-13.
- [3] Barman, A., Weakly symmetric and weakly Ricci-symmetric LP-Sasakian manifolds admitting a quarter-symmetric metric connection.
Novi Sad J. Math. 45 (2015), no. 2, 143-153.
- [4] Cartan, E., Sur une classe remarquable d’espaces de Riemannian. Bull. Soc. Math. France 54 (1926), 214-264.
- [5] Chaubey, S. K. and Ojha, R. H., On semi-symmetric non-metric and quarter-symmetric metric connections. Tensor N. S. 70 (2008), no. 2,
202-213.
- [6] Chaubey, S. K., Lee, J.W. and Yadav, S., Riemannian manifolds with a semi-symmetric metric P-connection. J. Korean Math. Soc. 56 (2019),
no. 4, 1113-1129.
- [7] De, U. C., Matsumoto, K. and Shaikh, A. A., On Lorentzian para-Sasakian manifolds. Rendiconti del Seminario Mat. de Messina 3 (1999),
149-156.
- [8] De, U. C., Velimirovic, L. and Mallick, S., On a type of spacetime. International Journal of Geometric Methods in Modern Physics 14 (2017), no.
1, 1750003 (9 pages).
- [9] Demirbag, S. A., Yilmaz, H. B., Uysal, S. A. and Zengin, F. O
:, On quasi Einstein manifolds admitting a Ricci quarter-symmetric metric
connection. Bull. of Math. Anal. and Appl. 3 (2011), no. 4, 84-91.
- [10] Ellis, G. F. R., Relativistic Cosmology in ’General Relativity and Cosmology’, ed. R. K. Sachs, Academic Press, London, 1971.
- [11] Eriksson, I. and Senovilla, J. M. M., Note on (conformally) semi-symmetric spacetimes. Class. Quantum Grav. 27 (2010), 027001.
- [12] Friedmann, A. and Schouten, J. A., Uber die Geometry der halbsymmetrischen Ubertragung. Math Zeitschr 21 (1924), 211-223.
- [13] Golab, S., On semi-symmetric and quarter-symmetric linear connections. Tensor N. S. 29 (1975), 249-254.
- [14] Guler, S. and Demirbag, S. A., A study of generalized quasi Einstein spacetimes with applications in general relativity. Int J Theor Phys 55
(2016), 548–562.
- [15] Hayden, H. A., Subspace of space with torsion. Proc. London Math. Soc. 34 (1932), 27-50.
- [16] Mantica, C. A., De, U. C., Suh, Y. J. and Molinari, L. G., Perfect fluid spacetimes with harmonic generalized curvature tensor. Osaka J.
Math. 56 (2019), 173-182.
- [17] Matsumoto, K., On Lorentzian para-contact manifolds. Bull. Yamagata Univ. Nat. Sci. 12 (1989), 151-156.
- [18] Matsumoto, K. and Mihai, I., On a certain transformation in a Lorentzian para-Sasakian manifold. Tensor N. S. 47 (1988), 189-197.
- [19] Mihai, I. and Rosca, R., On Lorentzian P-Sasakian manifolds. Classical Analysis, World Scientific Publi., Singapore (1992), 155-169.
- [20] Mihai, I., De, U. C. and Shaikh, A. A., On Lorentzian para-Sasakian manifolds. Korean J. Math. Sci. 6 (1999), 1-13.
- [21] Mishra, R. S. and Pandey, S. N., On quarter symmetric metric F-connections. Tensor N. S. 34 (1980), 1-7.
- [22] Murathan, C., Yildiz, A., Arslan, K. and De, U. C., On a class of Lorentzian para-Sasakian manifolds. Proc. Estonian Acad. Sci. Phys. Math.
55 (2006), no. 4, 210-219.
- [23] Rastogi, S. C., On quarter-symmetric metric connection. C. R. Acad. Bulg. Sci. 31 (1978), no. 8, 811-814.
- [24] Patterson, E. M., Some theorems on Ricci-recurrent spaces. J. London Math. Soc. 27 (1952), 287-295.
- [25] Prasad, R. and Haseeb, A., On a Lorentzian para-Sasakian manifold with respect to the quarter-symmetric metric connection. Novi Sad J.
Math. 46 (2016), no. 2, 103-116.
- [26] Srivastava, S. K., Scale factor dependent equation of state for curvature inspired dark energy, phantom barrier and late cosmic
acceleration. Physics Letters B 643 (2006), 1-4.
- [27] Sular, S., O
zgur, C. and De, U. C., Quarter-symmetric metric connection in a Kenmotsu manifold. SUT Journal of Mathematics 44 (2008),
297-306.
- [28] Szabó, Z. I., Structure theorems on Riemannian spaces satisfying R(X; Y ) R = 0: I. The local version. J. Diff. Geom 17 (1982), 531-582.
- [29] Weyl, H., Reine Infinitesimalgeometrie. Math. Z. 2 (1918), 384-411.
- [30] Zengin, F. O
.,M-projectively flat spacetimes. Math. Rep. 4 (2012), no. 4, 363–370.