Some Curvature properties on Trans-Sasakian Manifolds

Authors

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

Keywords:

Trans-Sasakian Manifolds, Concircular Curvature Tensor, Einstein.

Abstract

In this paper we show that the trans-Sasakian manifolds satisfying the condition R(X, Y ) · S = 0 is an Einstein manifold. Finally, we show that R · C˜ = R · R

References

  1. C. S.Bagewadi and Venkatesha, Some Curvature Tensors on a Trans-Sasakian Manifold, Turk. J. Math., 31, 111- 121, (2007).
  2. C.S.Bagewadi and Venkatesha, Torseforming vector field in a 3-dimensional Trans-Sasakian Manifold, Differential Geometry-Dynamical Systems, 8, 23-28, (2006).
  3. D.E.Blair and J.A.Oubina, Conformal and related changes of metric on the product of two almost contact metric manifolds, Publ. Matematiques, 34, 199-207, (1990).
  4. U.C.De and M.M.Tripathi, Ricci tensor in 3-dimensional trans-Sasakian manifolds, Kyung- pook Math. J. 43, No.2, 247-255, (2003).
  5. J.C.Marrero, The local structure of Trans-Sasakian manifolds, Annali di Matematica pura ed applicata. CLXII, 77-86, (1992).
  6. J.A.Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen, 32, 187-193, (1985).
  7. A.A.Shaikh, K.K.Baishya and Eyasmin, On D-homothetic deformation of trans-Sasakian structure, Demonstr.
  8. Math., XLI(1), 171-188, (2008).
  9. A.Taleshian and N.Asghari, On LP-Sasakian manifolds satisfying certain conditions on the Concircular curvature tensor, Differential Geometry-Dynamical Systems, 12, 228-232, (2010).
  10. M.M.Tripathi, Trans-Sasakian manifolds are generalised quasi-Sasakian, Nepali Math.Sci. Rep., 18, No.1-2, 11-14, (2001).

Downloads

Published

2017-04-30

Issue

Section

Research Articles

How to Cite

[1]
S.N. Manjunath, K.J. Jayashree, P. Rashmi "Some Curvature properties on Trans-Sasakian Manifolds " International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 3, Issue 2, pp.1016-1020, March-April-2017.