Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

Some Symmetric Properties on (LCS)n-manifolds

  • Received : 2013.10.03
  • Accepted : 2014.05.21
  • Published : 2015.03.23
Download PDF
⟨ Previous Next ⟩

Abstract

We analyze the $(LCS)_n$-manifolds endowed with some symmetric properties, focusing on Ricci tensor and the 1-form ${\gamma}$. We study some properties of special Weakly Ricci-Symmetric $(LCS)_n$-manifolds and also shown that Weakly ${\phi}$-Ricci Symmetric $(LCS)_n$-manifold is an ${\eta}$-Einstein manifold.

Keywords

References

  1. A. Bhagwat Prasad, A Pseudo Projective Curvature Tensor on a Riemannian Manifolds, Bull. Cal. Math. Soc., 94(3)(2002), 163-166.
  2. E. Cartan, Sur une classe remarquable despaces de Riemannian, Bull. Soc. Math., France, 54(1926), 214-264.
  3. U. C. De and D. Tarafdar, On a type of new tensor in a Riemannian manifold and its relativistic significance, Ranchi Univ. Math. J., 24(1993), 17-19.
  4. U. C. De and S. Bandyopadhyay, On weakly symmetric Riemannian spaces, Publi. Math. Debrecen., 54(1999), 377-381.
  5. U. C. De, A. A. Shaikh and S. Biswas, On weakly symmetric contact metric manifolds, Tensor, N. S., 64(2003), 170-175.
  6. K. Matsumoto, On Lorentzian paracontact manifolds, Bull. of Yamagata Univ. Nat. Sci., 12(2)(1989), 151-156.
  7. G. P. Pokhariyal and R. S. Mishra, Curvature tensors and their relativistics significance, Yokohama Mathematical Journal, 18(1970), 105-108.
  8. J. A. Schouten, Ricci Calculas(second Edition), Springer-Verlag., (1954), 322.
  9. A. A. Shaikh, orentzian almost paracontact manifolds with a structure of concircular type, Kyungpook Math. J., 43(2)(2003), 305-314.
  10. A. A. Shaikh and S. K. Jana, On weakly symmetric manifolds, Publi. Math. Debrecen., 71/1-2(2007), 27-41.
  11. A. A. Shaikh and S. K. Jana, On weakly Cyclic Ricci symmetric manifolds, Ann. Polon. Math., 89(2006), 273-288. https://doi.org/10.4064/ap89-3-4
  12. S. S. Shukla and Mukesh Kumar Shukla, On ${\phi}$-ricci symmetric kenmotsu manifolds, Novi Sad J. Math., 39(2)(2009), 89-95.
  13. L. Tamassy and T. Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, Colloq. Math. Janos Bolyai., 56(1989), 663-670.
  14. L. Tamassy and T. Q. Binh, On weakly symmetries of Einstein and Sasakian manifolds, Tensor, N. S., 53(1993), 140-148.
  15. Venkatesha and C. S. Bagewadi, On concircular ${\phi}$-recurrent LP-Sasakian manifolds, Differ. Geom. Dyn. Syst., 10(2008), 312-319.
  16. Venkatesha, C. S. Bagewadi and K. T. Pradeep Kumar, Some results on Lorentzian para-Sasakian manifolds, ISRN Geometry, 2011(2011), 9 pages.
  17. K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics, World Scientific, Singapore, 3(1984).
  18. K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Differential Geometry, 2(1968), 161-184.