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Journals / International Electronic Journal of Geometry / 2019 / Cilt: 12 - Sayı: 2

Lorentzian para-Sasakian Manifolds Admitting a New Type of Quarter-symmetric Non-metric ξ-connection

S. K. CHAUBEY
Uday Chand DE
Pages
250–259
Publication Date
2019-10-03
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

To validate the existence of the quarter-symmetric non-metric $\xi$-connection on an $LP$-Sasakian manifold, we give a non-trivial example in dimension $4$ and verify our results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We define a new type of quarter-symmetric non-metric $\xi$-connection on an $LP$-Sasakian manifold and prove its existence.
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Key Findings & Data:We provide its application in the general theory of relativity.
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Conclusion & Impact:To validate the existence of the quarter-symmetric non-metric $\xi$-connection on an $LP$-Sasakian manifold, we give a non-trivial example in dimension $4$ and verify our results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Lorentzian para-Sasakian manifold · quarter-symmetric non-metric connection · conformal curvature tensors

Abstract

We define a new type of quarter-symmetric non-metric $\xi$-connection on an $LP$-Sasakian manifold and prove its existence. We provide its application in the general theory of relativity. To validate the existence of the quarter-symmetric non-metric $\xi$-connection on an $LP$-Sasakian manifold, we give a non-trivial example in dimension $4$ and verify our results.

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Cite This Article

CHAUBEY, S. K., DE, U. C. (2019). Lorentzian para-Sasakian Manifolds Admitting a New Type of Quarter-symmetric Non-metric ξ-connection. International Electronic Journal of Geometry, Cilt: 12 - Sayı: 2, 250–259. https://ajindex.com/articles/672082

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References (1)

  1. K. Arslan, R. Deszcz, R. Ezentas, M. Hotlo$\acute{s}$ and C. Murathan, On generalized Robertson-Walker spacetimes satisfying some curvature condition, Turk J Math 38 (2014), 353-373. Reference2A. A. Aqeel, U. C. De and G. C. Ghosh, On Lorentzian para-Sasakian manifolds, Kuwait J. Sci. Eng. 31 (2) (2004), 1-13. Reference3A. Barman, Weakly symmetric and weakly Ricci-symmetric $LP$-Sasakian manifolds admitting a quarter-symmetric metric connection, Novi Sad J. Math. 45 (2) (2015), 143-153. Reference4E. Cartan, Sur une classe remarquable d’espaces de Riemannian, Bull. Soc. Math. France 54 (1926), 214-264. Reference5S. K. Chaubey and R. H. Ojha, On semi-symmetric non-metric and quarter-symmetric metric connections, Tensor N. S. 70 2 (2008), 202-213. Reference6U. C. De, K. Matsumoto and A. A. Shaikh, On Lorentzian para-Sasakian manifolds, Rendiconti del Seminario Mat. de Messina(3) (1999), 149-156. Reference7U. C. De, L. Velimirovi$\acute{c}$ and S. Mallick, On a type of spacetime, International Journal of Geometric Methods in Modern Physics 14 (1) (2017) 1750003 (9 pages). Reference8S. A. Demirba$\breve{g}$, H. B. Yilmaz, S. A. Uysal and F. $\ddot{O}.$ Zengin, On quasi Einstein manifolds admitting a Ricci quarter-symmetric metric connection, Bull. of Math. Anal. and Appl., 3 (4), (2011), 84-91. Reference9G. F. R. Ellis, Relativistic Cosmology in ’General Relativity and Cosmology’, ed. R. K. Sachs (Academic Press, London, 1971). Reference10I. Eriksson and J. M. M. Senovilla, Note on (conformally) semi-symmetric spacetimes, Class. Quantum Grav. 27 027001 (2010). Reference11 A. Friedmann and J. A. Schouten, Uber die Geometry der halbsymmetrischen Ubertragung. Math Zeitschr 21 (1924), 211-223. Reference12S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor, N.S., 29 (1975), 249-254. Reference13S. G$\ddot{u}$ler and S. A. Demirba$\breve{g}$, A study of generalized quasi Einstein spacetimeswith applications in general relativity, Int J Theor Phys 55 (2016), 548–562. Reference14 H. A. Hayden, Subspace of space with torsion. Proc. London Math. Soc. 34, 27-50 (1932). Reference15C. A. Mantica, U. C. De, Y. J. Suh and L. G. Molinari, Perfect fluid spacetimes with harmonic generalized curvature tensor, Osaka J. Math.56 (2019), 173-182. Reference16K. Matsumoto, On Lorentzian para contact manifolds, Bull. Yamagata Univ. Nat. Sci. 12 (1989), 151-156. Reference17K. Matsumoto and I. Mihai, On a certain transformation in a Lorentzian para-Sasaki