Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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CERTAIN CURVATURE CONDITIONS IN KENMOTSU MANIFOLDS WITH RESPECT TO THE SEMI-SYMMETRIC METRIC CONNECTION

  • Haseeb, Abdul (Department of Mathematics Faculty of Science Jazan University) ;
  • Prasad, Rajendra (Department of Mathematics and Adtronomy University of Lucknow)
  • Received : 2016.12.17
  • Accepted : 2017.05.30
  • Published : 2017.10.31
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Abstract

The conharmonic curvature tensor under certain conditions has been studied for Kenmotsu manifolds with respect to the semi-symmetric metric connection.

Keywords

References

  1. Z. Ahsan, Relativistic significance of conharmonic curvature tensor, Maths. Today 16(A) (1998), 23-28.
  2. Z. Ahsan, Tensors: Mathematics of Differential Geometry and Relativity, Prentice Hall of India Learning Pvt. Ltd., Delhi, 2015.
  3. N. Asghari and A. Taleshian, On the conharmonic curvature tensor of Kenmotsu manifolds, Thai J. Math. 12 (2014), no. 3, 525-536.
  4. A. Barman and U. C. De, Projective curvature tensor of a semi-symmetric metric connection in a Kenmotsu manifold, Int. Electron. J. Geom. 6 (2013), no. 1, 159-169.
  5. A. Barman and U. C. De, Semi-symmetric non-metric connections on Kenmotsu manifolds, Roumanian J. Math. Comp. Sci. 5 (2015), no. 1, 13-24.
  6. U. C. De and S. C. Biswas, On a type of semi-symmetric metric connection on a Riemannian manifold, Publ. Inst. Math. (Beogran) (N. S.) 61(75) (1997), 90-96.
  7. U. C. De and G. Pathak, On 3-dimensional Kenmotsu manifolds, Indian J. Pure Appl. Math. 35 (2004), no. 2, 159-165.
  8. A. Friedmann and J. A Schouten, Uber die Geometrie der halbsymmetrischen Ubertragung, Math. Z. 21 (1924), no. 1, 211-223. https://doi.org/10.1007/BF01187468
  9. 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. Comenian. 85 (2016), no. 1, 9-20.
  10. H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc. 34 (1932), 27-50.
  11. Y. Ishii, On conharmonic transformations, Tensor (N. S.) 7 (1957), 73-80.
  12. J. B. Jun, U. C. De, and G. Pathak, On Kenmotsu manifolds, J. Korean Math. Soc. 42 (2005), no. 3, 435-445. https://doi.org/10.4134/JKMS.2005.42.3.435
  13. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), no. 1, 93-103. https://doi.org/10.2748/tmj/1178241594
  14. C. Ozgur, M. Ahmad, and A. Haseeb, CR-submanifolds of a Lorentzian para-Sasakian manifold with a semi-symmetric metric connection, Hacet. J. Math. Stat. 39(2010), no. 4, 489-496.
  15. G. Pathak and U. C. De, On a semi-symmetric connection in a Kenmotsu manifold, Bull. Calcutta Math. Soc. 94 (2002), no. 4, 319-324.
  16. S. A. Siddiqui and Z. Ahsan, Conharmonic curvature tensor and the spacetime of general relativity, Differ. Geom. Dyn. Syst. 12 (2010), 213-220.
  17. S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J. 21 (1969), no. 2, 21-38. https://doi.org/10.2748/tmj/1178243031
  18. K. Yano, On semi-symmetric metric connections, Rev. Roumainae Math. Pures Appl. 15 (1970), 1579-1586.
  19. K. Yano and M. Kon, Structures on Manifolds, World Scientific Publishing Co., Singapore, 1984.
  20. A. Yildiz and U. C. De, On a type of Kenmotsu manifolds, Differ. Geom. Dyn. Syst. 12 (2010), 289-298.