Some Curvature Properties of K-Contact Manifolds with Semi-Symmetric Non-Metric Connections

Authors

  • S. N. Manjunath  Lecturer, Department of Science, Govt. VISSJ Polytechnic, Bhadravathi, Karnataka, India
  • K. J. Jayashree  Senior Scale Lecturer, Department of Science, Govt. Polytechnic, Hiriyur, Karnataka, India
  • P. Rashmi  Lecturer, Department of Science, Govt. Polytechnic, Tumkur, Karnataka, India

Keywords:

Semi-Symmetric Non-Metric Connection, K-Contact Manifold, Conformal Curvature Tensor.

Abstract

In this paper we define a linear connection on a K-contact manifold which is semi-symmetric but non-metric and we study some properties of the Riemannian curvature tensor, conformal curvature tensor with respect to semi-symmetric non-metric connection.

References

  1. N.S. Agashe and M.R. Chafle, A semi-symmetric non-metric connection in a Riemannian manifold, Indian J. Pure Appl. Math. 23 (1992), 399-409.
  2. N.S. Agashe and M.R. Chafle, On submanifolds of a Riemannian manifold with semi-symmetric non-metric connection, Tensor N.S., 55 (2) (1994), 120-130.
  3. K.S. Amur and S.S. Pujar, On Submanifolds of a Riemannian manifold admitting a metric semi-symmetric connection , Tensor, N.S., 32 (1978), 35-38.
  4. C.S. Bagewadi, D.G. Prakasha and Venkatesha, Projective curvature tensor on a Kenmotsu manifold with respect to semi-symmetric metric connection, Stud. Cercet. Stiint. Ser. Mat. Univ. Bacau., 17 (2007), 21-32.
  5. C.S. Bagewadi and Gurupadavva Ingalahalli, A Study on ϕ-Symmetric K-contact manifold admitting Quarter-Symmetric metric connection, Journal of Mathematical Physics, Analysis, Geometry, 10 (4), (2014), 1-13.
  6. S.C. Biswas and U.C. De, On a type of semi-symmetric non-metric connection on a Riemannian manifold, Ganita. 48 (1997), 91-94.
  7. D.E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Vol.509. Springer-Verlag, berlin-New-York, 1976.
  8. S.K. Chaubey and R.H. Ojha, On a semi-symmetric non-metric connection, Filomat, 25 (4) (2011), 19-27.
  9. S.K. Chaubey, Almost Contact metric manifolds admitting semi-symmetric non-metric connection, Bulletin of Mathematical Analysis and Applications, 2 (2011), 252-260.
  10. U.C. De and Joydeep Sengupta, On a type of semi-symmetric metric connection on an contact metric manifold, Filomat, 14 (2000), 33-42.
  11. U.C. De and G. Pathak, On a semi-symmetric metric connection in a Kenmotsu manifolds, Bull. Calcutta Math. Soc., 94 (40) (2002), 319-324.
  12. A. Friedmann and J.A. Schouten, Uber die geometrie der halbsymmetrischen Ubertragung, Math. Zeitscr., 21 (1924), 211-223.
  13. Gurupadavva Ingalahalli and C.S. Bagewadi, A study on Conservative C-Bochner curvature tensor in K-contact and Kenmotsu manifolds admitting semi-symmetric metric connection, ISRN Geometry, (2012), 14 pages.
  14. Gurupadavva Ingalahalli and C.S. Bagewadi, On φ-Symmetry of C-Bochner curvature tensor in para-Sasakian manifold admitting Quarter-Symmetric metric connection, Asian Journal of Mathematics and Computer Research, 17 (3), (2017), 172-183.
  15. H.A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc., 34 (1932), 27-50.
  16. J.P. Jaiswal and R.H. Ojha, Some properties of K-contact Riemannian manifolds admitting a semi-symmetric non-metric connections, Filomat, 24 (4) (2010), 9-16.
  17. Selcen Yuksel Perktas, Erol Kilic, Sadik Keles, On a semi-symmetric non-metric connection in an LP-Sasakian manifold, International Electronic Journal of Geometry, 3 (2) (2010), 15-25.
  18. J. Sengupta, U.C. De and T.Q. Binh, On a type of semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 31 (12) (2000), 1659-1670.
  19. M.M. Tripathi and N. Nakkar, On a semi-symmetric non-metric connection in a Kenmotsu manifold, Bull. Cal. Math. Soc. 16 (4) (2001), 323-330.
  20. M.M. Tripathi, A new connection in a Riemannian manifold, International Electronic Journal of Geometry. 1 (1) (2008), 15-24.
  21. K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Differential Geometry, 2 (1968), 161-184.
  22. K. Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579-1586.

International Journal of Scientific Research in Science and Technology

Downloads

Published

2020-10-30

Issue

Volume 7, Issue 5, September-October-2020

Section

Research Articles

License

Copyright (c) IJSRST

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
S. N. Manjunath, K. J. Jayashree, P. Rashmi "Some Curvature Properties of K-Contact Manifolds with Semi-Symmetric Non-Metric Connections" International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011,Volume 7, Issue 5, pp.429-435, September-October-2020.