Generalized quasi-conformal curvature tensor and the spacetime of general relativity
Resumo
In this paper, a study of generalized quasi-conformal curvature tensor has been made on the four dimensional spacetime of general relativity. Some results related to the application of such spacetime in the general relativity are obtained. Perfect fluid and dust fluid cosmological models have also been studied.
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Referências
Ahsan, Z. and Siddiqui, S. A., Concircular curvature tensor and fluid space-times, Int. J. Theor. Phys., 48, 3202–3212, (2009).
Amendola, L. and Tsujikawa, S., Dark Energy-Theory and Observations, Cambridge University Press, Cambridge, (2010).
Angadi, P. G., Shivaprasanna, G. S., Somashekhara, G. and Siva Kota Reddy, P., Ricci-Yamabe Solitons on Submanifolds of Some Indefinite Almost Contact Manifolds, Adv. Math., Sci. J., 9(11), 10067-10080, (2020).
Angadi, P. G., Shivaprasanna, G. S., Somashekhara, G. and Siva Kota Reddy, P., Ricci Solitons on (LCS)-Manifolds under D-Homothetic Deformation, Italian Journal of Pure & Applied Mathematics, 46, 672-683, (2021).
Angadi, P. G., Siva Kota Reddy, P., Shivaprasanna, G. S. and Somashekhara, G., On Weakly Symmetric Generalized (k, μ)-Space Forms, Proceedings of the Jangjeon Math. Soc., 25(2), 133-144, (2022).
Baishya, K. K., GRW-space-time and certain type of energy-momentum tensor, Journal of Geometry and Physics, 157, Article Id. 103855, (2020).
Chaki, M. C. and Ray, S, Space-times with covariant-constant energy-momentum tensor, International Journal of Theoretical Physics, 35(5), 1027-1032, (1996).
Duggal, K. L., Curvature collineations and conservation laws of general relativity, Presented at the Canadian Conference on General Relativity and Relativistic Astrophysics, Halifax, Canada, (1985).
Duggal, K. L., Curvature inheritance symmetry in Riemannian spaces with applications to fluid spacetimes, J. Math. Phys., 33, 2989-2997, (1992).
Katzin, G. H., Levine, J. and Davis, W. R., Curvature collineations: a fundamental property of the space-times of general relativity defined by the vanishing Lie derivative of the Riemann curvat ure tensor, J. Math. Phys., 10, 617-629, (1969).
Mazumder, N., Biswas, R. and Chakraborty, S., Cosmological evolution across phantom crossing and the nature of the horizons, Astrophys Space Sci, 334, 183-186, (2011).
O’Neill B., Semi-Riemannian geometry with applications to relativity, Academic Press, New York-London, (1983).
Sach, R. K. and Hu, W., General Relativity for Mathematician, Springer Verlag, New York, (1977).
Somashekhara, G., Pavani, N. and Siva Kota Reddy, P., Invariant Sub-manifolds of LP-Sasakian Manifolds with Semi-Symmetric Connection, Bull. Math. Anal. Appl., 12(2), 35-44, (2020).
Somashekhara, G., Girish Babu, S. and Siva Kota Reddy, P., Indefinite Sasakian Manifold with Quarter-Symmetric Metric Connection, Proceedings of the Jangjeon Math. Soc., 24(1), 91-98, (2021).
Somashekhara, G., Girish Babu, S. and Siva Kota Reddy, P., Conformal Ricci Soliton in an Indefinite Trans-Sasakian manifold, Vladikavkaz Math. J, 23(3), 43-49, (2021).
Somashekhara, G., Girish Babu, S. and Siva Kota Reddy, P., Ricci Solitons and Generalized Weak Symmetries under D-Homothetically Deformed LP-Sasakian Manifolds, Italian Journal of Pure & Applied Mathematics, 46, 684–695, (2021).
Somashekhara, G., Girish Babu, S. and Siva Kota Reddy, P., Conformal -Ricci Solitons in Lorentzian Para-Sasakian Manifold Admitting Semi-Symmetric Metric Connection, Italian Journal of Pure & Applied Mathematics, 46, 1008-1019, (2021).
Somashekhara, G., Siva Kota Reddy, P., Shivashankara, K. and Pavani, N., Slant Sub-manifolds of Generalized Sasakian-Space-Forms, Proceedings of the Jangjeon Math. Soc., 25(1), 83–88, (2022).
Somashekhara, G., Girish Babu, S., Siva Kota Reddy, P., and Shivashankara, K., On LP-Sasakian Manifolds admitting Generalized Symmetric Metric Connection, Proceedings of the Jangjeon Math. Soc., 25(3), 287-296, (2022).
Somashekhara, G., Girish Babu, S. and Siva Kota Reddy, P., -Ricci soliton in an indefinite trans-Sasakian manifold admitting semi-symmetric metric connection, Bol. Soc. Parana. Mat. (3), 41, 1-9, (2023).
Somashekhara, G., Rajendra, R., Shivaprasanna, G. S. and Siva Kota Reddy, P., Pseudo Parallel and Generalized Ricci Pseudo Parallel Invariant Submanifolds of a Generalized Sasakian Space Form, Proceedings of the Jangjeon Math. Soc., 26(1), 69-78, (2023).
Srivastava, S. K., General Relativity and Cosmology, PHI Learning, New Delhi, (2008).
Stephani, H., Kramer, D., MacCallum, M., Hoenselaers, C. and Herlt, E., Exact Solutions of Einstein’s Field Equations, Second Edition. 732 p., Cambridge University Press, Cambridge, (2003).
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