DOI QR코드

DOI QR Code

CERTAIN CURVATURE CONDITIONS IN KENMOTSU MANIFOLDS

  • Haseeb, Abdul (Department of Mathematics, Faculty of Science, Jazan University)
  • 투고 : 2019.08.21
  • 심사 : 2019.11.19
  • 발행 : 2020.06.25

초록

The objective of the present paper is to study certain curvature conditions in Kenmotsu manifolds with respect to the semi-symmetric non-metric connection. Finally, we construct an example of 5-dimensional Kenmotsu manifold with respect to the semi-symmetric non-metric connection to verify some results of the paper.

키워드

참고문헌

  1. A. A. Shaikh and S. K. Jana, A pseudo-quasi-conformal curvature tensor on a Riemannian manifold, South East Asian J. Math. Sci., 4(2005), 15-20.
  2. A. Barman and U. C. De, Semi-symmetric non-metric connections on Kenmotsu manifolds, Romanian J. Math. Comp. Sci., 5(2014), 13-24.
  3. A. Friedmann and J. A. Schouten, Uber die Geometric der halbsymmetrischen Ubertragung, Math. Z., 21(1924), 211-223. https://doi.org/10.1007/BF01187468
  4. A. Haseeb, On concircular curvature tensor with respect to the semi-symmetric non-metric connection in a Kenmotsu manifold, Kyungpook Math. J., 56(2016), 951-964. https://doi.org/10.5666/KMJ.2016.56.3.951
  5. A. Haseeb, M. A. Khan and M. D. Siddiqi, Some more results on an $\epsilon$-Kenmotsu manifold with a semi-symmetric metric connection, Acta Math. Univ. Comenianae, 85(2016), 9-20.
  6. A. Yildiz and U. C. De, On a type of Kenmotsu manifolds, Differ. Geom. Dyn. Syst., 12(2010), 289-298.
  7. D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag Berlin-New York, 1976.
  8. H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc., 34(1932), 27-50. https://doi.org/10.1112/plms/s2-34.1.27
  9. J. B. Jun, U. C. De and G. Pathak, On Kenmotsu manifolds, J. Korean Math. Soc., 42(2005), 435-445. https://doi.org/10.4134/JKMS.2005.42.3.435
  10. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J., 24(1972), 93-103. https://doi.org/10.2748/tmj/1178241594
  11. K. Yano, On semi-symmetric metric connection, Revue Roumaine de Math. Pures Appl., 15(1970), 1579-1586.
  12. L. S. Das, M. Ahmad and A. Haseeb, On semi-invariant submanifolds of a nearly Sasakian manifold admitting a semi-symmetric non-metric connection, Journal of Applied Analysis, 17(2011), 119-130. https://doi.org/10.1515/JAA.2011.007
  13. N. Asghari and A. Taleshian, On the conharmonic curvature tensor of Kenmotsu manifolds, Thai J. Math., 12(2014), 525-536.
  14. N. S. Agashe and M. R. Chae, A semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math., 23(1992), 339-409.
  15. S. S. Shukla and M. K. Shukla, On ${\phi}$-Ricci symmetric Kenmotsu manifolds, Novi Sad J. Math., 39(2009), 89-95.
  16. U. C. De and S. C. Biswas, On a type of semi-symmetric non-metric connection on a Riemannian manifold, Ganita, 48(1997), 91-94.