Honam Mathematical Journal (호남수학학술지)

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SOME NOTES ON LP-SASAKIAN MANIFOLDS WITH GENERALIZED SYMMETRIC METRIC CONNECTION

  • Bahadir, Oguzhan (Department of Mathematics, Faculty of Arts and Sciences) ;
  • Chaubey, Sudhakar K. (Section of Mathematics, Department of Information Technology, Shinas College of Technology)
  • Received : 2019.10.11
  • Accepted : 2020.01.12
  • Published : 2020.09.25
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Abstract

The present study initially identify the generalized symmetric connections of type (α, β), which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when (α, β) = (1, 0) and (α, β) = (0, 1). Taking that into account, a new generalized symmetric metric connection is attained on Lorentzian para-Sasakian manifolds. In compliance with this connection, some results are obtained through calculation of tensors belonging to Lorentzian para-Sasakian manifold involving curvature tensor, Ricci tensor and Ricci semi-symmetric manifolds. Finally, we consider CR-submanifolds admitting a generalized symmetric metric connection and prove many interesting results.

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References

  1. N. S. Agashe and M. R. Chafle, A semi symetric non-metric connection in a Riemannian manifold, Indian J. Pure Appl. Math. 23 (1992), 399-409.
  2. O. Bahadir, Lorentzian para-Sasakian manifold with quartersymmetric non-metric connection, Journal of Dynamical Systems and Geometric Theories 14(1) (2016), 17-33. https://doi.org/10.1080/1726037X.2016.1177920
  3. S. K. Chaubey, Some properties of LP-Sasakian manifolds equipped with m-projective curvature tensor, Bulletin of Math. Analysis and Applications 3(4) (2011), 50-58.
  4. S. K. Chaubey and U. C. De, Characterization of the Lorentzian para-Sasakian manifolds admitting a quarter-symmetric non-metric connection, SUT Journal of Mathematics 55(1) (2019), 53-67.
  5. S. K. Chaubey and U. C. De, Lorentzian para-Sasakian manifolds admitting a new type of quarter-symmetric non-metric ${\xi}$-connection, Int. Electron. J. Geom. 12(2) (2019), 250-259. https://doi.org/10.36890/iejg.548364
  6. S. K. Chaubey and A. Yildiz, Riemannian manifolds admitting a new type of semi-symmetric non-metric connection, Turk J Math. 43 (2019), 1887-1904. https://doi.org/10.3906/mat-1902-2
  7. S. K. Chaubey and R. H. Ojha, On a semi-symmetric non-metric connection, Filomat 26(2) (2012), 63-69.
  8. S. K. Chaubey and R. H. Ojha, On semi-symmetric non-metric and quarter-symmetric metric connections, Tensor N. S. 70(2) (2008), 202-213.
  9. S. K. Chaubey, J. W. Lee and S. Yadav, Riemannian manifolds with a semi-symmetric metric P-connection, J. Korean Math. Soc. 56(4) (2019), 1113-1129. https://doi.org/10.4134/jkms.j180642
  10. M. Danish Siddiqi, M. Ahmad and J. P. Ojha, CR-submanifolds of a nearly trans-hyperbolic Sasakian manifold with a semi-symmetric non-metric connection, Afr. Diaspora J. Math. (N.S.) 17 (2014), 93-105.
  11. U. C. De and D. Kamilya, Hypersurfaces of Rieamnnian manifold with semi-symmetric non-metric connection, J. Indian Inst. Sci. 75 (1995), 707-710.
  12. U. C. De and A. K. Sengupta, CR-submanifolds of a Lorentzian para-Sasakian manifold, Bull. Malaysian Math. Sci. Soc. 23 (2000), 99-106.
  13. S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor N. S. 29 (1975), 249-254.
  14. A. Haseeb and R. Prasad, ${\eta}$-Ricci solitons on ${\epsilon}$-LP-Sasakian manifolds with a quarter-symmetric metric connection, Honam Mathematical J. 41(3) (2019), 539-558. https://doi.org/10.5831/hmj.2019.41.3.539
  15. H. A. Hayden, Subspaces of a space with torsion, London Math. Soc. 34 (1932), 27-50. https://doi.org/10.1112/plms/s2-34.1.27
  16. S. K. Hui, S. Uddin, C. Ozel and A. A. Mustafa, Warped product submanifolds of LP-Sasakian manifolds, Hindawi Publishing Corporation, Discrete Dynamics in Nature and Society 2012, Article ID 868549, 11 pages.
  17. D. H. Jin, Lightlike hypersurfaces of an indefinite Kaehler manifold with a symmetric metric connection of type (l,m), Bull. Korean Math. Soc. 53(4) (2016), 1171-1184. https://doi.org/10.4134/BKMS.b150590
  18. Y. Liang, On semi-symmetric recurrent-metric connection, Tensor N. S. 55 (1994), 107-112.
  19. J. W. Lee, C. W. Lee and D. W. Yoon, Inequalities for generalized ${\delta}$-Casorati curvatures of submanifolds in real space forms endowed with a semi-symmetric metric connection, Revista De La Union Matematica Argentina 57(2) (2016), 53-62.
  20. C. W. Lee, J. W. Lee and G. E. Vilcu and D. W. Yoon, Optimal inequalities for the Casorati curvatures of submanifolds of generalized space forms endowed with semi-symmetric metric connections, Bull. Korean Math. Soc. 52(5) (2015), 1631-1647. https://doi.org/10.4134/BKMS.2015.52.5.1631
  21. K. Matsumoto, On Lorentzian Paracontact manifolds, Bull. Yamagata Univ. Natur. Sci. 12(2) (1989), 151-156.
  22. K. Matsumoto and I. Mihai On a certain transformation in a Lorentzian para Sasakian manifold, Tensor N. S. 47 (1988), 189-197.
  23. I. Mihai and R. Rosca, On Lorentzian P-Sasakian manifolds, Clssical Analysis, World Scientific Publ. 1992, 155-169.
  24. I. Mihai, A. A. Shaikh and U. C. De, On Lorentzian para-Sasakian manifolds, Rendiconti del Seminario Mat. di Messina, Serie II, 1999.
  25. C. Ozgur, M. Ahmad and A. Haseeb, CR-submanifolds of a Lorentzian para-Sasakian manifold with a semi-symmetric metric connection, Hacettepe Journal of Mathematics and Statistics 39(4) (2010), 489-496.
  26. S. Pahan, B. Pal and A. Bhattacharyya, On Einstein warped products with a quarter-symmetric connection, International Journal of Geometric Methods in Modern Physics 14 (2017), 1750050. https://doi.org/10.1142/S0219887817500505
  27. S. Pahan, B. Pal and A. Bhattacharyya, On Ricci flat warped products with a quarter-symmetric connection, J. Geom. 107 (2016), 627-634. https://doi.org/10.1007/s00022-015-0301-3
  28. Q. Qu and Y. Wang, Multiply warped products with a quarter-symmetric connection, Journal of Mathematical Analysis and Applications 431(2) (2015), 955-987. https://doi.org/10.1016/j.jmaa.2015.06.011
  29. A. A. Shaikh and K. K. Baishya, On ${\Phi}$-symmetric LP-Sasakian manifolds, Yokohama Mathematical Journal 52 (2006), 97-112.
  30. B. G. Schmidt, Conditions on a connection to be a metric connection, Commun. Math. Phys. 29 (1973), 55-59. https://doi.org/10.1007/BF01661152
  31. M. M. Tripathi, A new connection in a Riemannian manifold, Int. Electron. J. Geom. 1 (2006), 15-24.
  32. S. K. Yadav, S. K. Chaubey and S. K. Hui, On the perfect fluid Lorentzian para-Sasakian spacetimes, Bulg. J. Phys. 46(1) (2018), 1-15.