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Journals / Konuralp Journal of Mathematics / 2019 / Volume: 7 Issue: 2

A Study on Lorentzian $\alpha -$Sasakian Manifolds

Rajendra Prasad(University of Lucknow, Lucknow)
Shashikant Pandey(University of Lucknow, Lucknow)
Sandeep Kumar Verma(University of Lucknow, Lucknow)
Sumeet Kumar(University of Lucknow, Lucknow)
Pages
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Publication Date
2019-10-15
DOI
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AI Summary & Key Takeaways

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

In the last, we provide an example of 3-dimensional Lorentzian $\alpha -$Sasakian manifold endowed with the quarter-symmetric metric connection which is under consideration is an $\eta -$Einstein manifold with respect to the quarter-symmetric metric connection.

📌 3 Key Takeaways

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Objective & Hypothesis:The object of the present paper is to study the geometric properties of Concircular curvature tensor on Lorentzian $\alpha -$Sasakian manifold admitting a type of quarter-symmetric metric connection.
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Key Findings & Data:The object of the present paper is to study the geometric properties of Concircular curvature tensor on Lorentzian $\alpha -$Sasakian manifold admitting a type of quarter-symmetric metric connection.
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Conclusion & Impact:In the last, we provide an example of 3-dimensional Lorentzian $\alpha -$Sasakian manifold endowed with the quarter-symmetric metric connection which is under consideration is an $\eta -$Einstein manifold with respect to the quarter-symmetric metric connection.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Lorentzian $\alpha $-Sasakian manifolds · Quarter-symmetric metric connection · Concircular curvature tensor

Abstract

The object of the present paper is to study the geometric properties of Concircular curvature tensor on Lorentzian $\alpha -$Sasakian manifold admitting a type of quarter-symmetric metric connection. In the last, we provide an example of 3-dimensional Lorentzian $\alpha -$Sasakian manifold endowed with the quarter-symmetric metric connection which is under consideration is an $\eta -$Einstein manifold with respect to the quarter-symmetric metric connection.

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Cite This Article

Prasad, R., Pandey, S., Verma, S. K., Kumar, S. (2019). A Study on Lorentzian $\alpha -$Sasakian Manifolds. Konuralp Journal of Mathematics, Volume: 7 Issue: 2. https://ajindex.com/articles/1521704

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References (18)

  1. A. Barman and G. Ghosh, Concircular curvature tensor of a semi-symmetric non-metric connection on P-Sasakian manifolds, An. Univ. Vest. Timis. Ser. Mat. Inform. LIV(2016), 47–58.
  2. D. E. Blair, Inversion theory and conformal mapping, Stud. Math. Libr. 9, Amer. Math. Soc. (2000).
  3. U. C. De and Krishnendu De, On Lorentzian Trans-Sasakian manifolds, Cummun. Fac. Sci. Univ. Ank. Series 62 (2013) no. 2, 37􀀀51:
  4. A. Friedmann and J. A. Schouten, ¨U ber die Geometric der halbsymmetrischen ¨U bertragung, Math. Z.21(1924), 211–223.
  5. S. Golab, On semi􀀀symmetric and quarter􀀀symmetric linear connections, Tensor (N.S.) 29 (1975); 249􀀀254.
  6. K. Matsumoto, On Lorentzian para-contact manifold, Bull Yomagata Univ. Natur. Sci. 12 no. 2 (1989) 151-156.
  7. W. Kuhnel, Conformal Transformations between Einstein Spaces, Bonn, 1985/1986, 105–146, Aspects Math. E12, Vieweg, Braunschweig, 1988.
  8. A.K. Mondal, U.C. De, Some properties of a quarter-symmetric metric connection on a Sasakian manifold. Bull. Math. Analysis Appl. 3 (2009), 99-108.
  9. K. Mandal and U.C. De, Quarter-symmetric metric connection in a P-Sasakian manifold. An. Univ. Vest. Timis. Ser. Math-Inform. LIII(2015), 137-150.
  10. O’Neill, B., Semi-Riemannian geometry with applications to relativity, Academic press (1983).
  11. C. Ozgur, f-conformally flat Lorentzian para-Sasakian manifolds. Radovi Matematicki 12 (2003), 99-106.
  12. R. Prasad and A. Haseeb, On a Lorentzian para-Sasakian manifold with respect to the quarter-symmetric metric connection, Novi Sad J. Math. Vol. 46, No. 2, 2016, 103-116.
  13. K. Yano, Concircular Geometry I. Concircular Transformations, Proc. Imp. Acad. Tokyo 16 (1940), 195–200.
  14. K. Yano and S. Bochner, Curvature and Betti numbers, Ann. of Math. Stud. 32(1953).
  15. A. Yildiz and C. Murathan, On Lorentzian a-Sasakian manifolds. Kyungpook Math. J. 45 (2005),95-103:
  16. A. Yildiz, M. Turan and B. E. Acet, On three dimensional Lorentzian a-Sasakian manifolds. Bull. Math. Anal. Appl. 1(2009), 90-98.
  17. A. Yildiz, M. Turan and C. Murathan, A class of Lorentzian a-Sasakian manifolds. Kyungpook Math. J. 49 (2009),789-799.
  18. S. Golab, On semi􀀀symmetric and quarter􀀀symmetric linear connections, Tensor (N.S.) 29 (1975); 249􀀀254.