Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

TRANS-SASAKIAN MANIFOLDS WITH RESPECT TO GENERALIZED TANAKA-WEBSTER CONNECTION

  • Kazan, Ahmet (Department of Computer Technologies, Dogansehir Vahap Kucuk Vocational School of Higher Education, Inonu University) ;
  • Karadag, H.Bayram (Department of Mathematics, Faculty of Arts and Sciences, Inonu University)
  • Received : 2018.02.26
  • Accepted : 2018.05.01
  • Published : 2018.09.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this study, we use the generalized Tanaka-Webster connection on a trans-Sasakian manifold of type (${\alpha},{\beta}$) and obtain the curvature tensors of a trans-Sasakian manifold with respect to this connection. Also, we investigate some special curvature conditions of a trans-Sasakian manifold with respect to generalized Tanaka-Webster connection and finally, give an example for trans-Sasakian manifolds.

Keywords

References

  1. B.E. Acet, E. Kilic and S.Y. Perktas, Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection, Int. J. of Math. and Math. Sci., doi:10.1155/2012/395462, (2012).
  2. C.S. Bagewadi and Venkatesha, Some Curvature Tensors on a Trans-Sasakian Manifold, Turk. J. Math. 31 (2007), 111-121.
  3. D.E. Blair and J.A. Oubina, Conformal and related changes of metric on the product of two almost contact metric manifolds, Publ. Mathematiques 34 (1990), 199-207.
  4. D.E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin-New York, 1976.
  5. U.C. De and A. Sarkar, On Three-Dimensional Trans-Sasakian Manifolds, Extracta Mathematicae 23(3) (2008), 265-277.
  6. U.C. De and K. De, On Lorentzian Trans-Sasakian Manifolds, Commun. Fac. Sci. Univ. Ank. Series A1 62(2) (2013), 37-51.
  7. U.C. De and M.M. Tripathi, Ricci tensor in 3-dimensional trans-Sasakian manifolds, Kyungpook Math. J. 2 (2003), 247-255.
  8. A. Gray and L.M. Hervella, The Sixteen classes of almost Hermitian manifolds and their Linear invariants, Ann. Mat. Pura Appl. 123(4) (1980), 35-58. https://doi.org/10.1007/BF01796539
  9. D. Janssens and L. Vanhecke, Almost Contact Structures and Curvature Tensors, Kodai Math. J. 4(1) (1981), 1-27. https://doi.org/10.2996/kmj/1138036310
  10. D.H. Jin, Lightlike Hypersurfaces of an Indefinite Trans-Sasakian Manifold with a Non-Metric ${\varphi}$-Symmetric Connection, Bull. Korean Math. Soc. 53(6) (2016), 1771-1783. https://doi.org/10.4134/BKMS.b150972
  11. J.A. Oubina, New Classes of almost Contact metric structures, Publ. Math. Debrecen 32 (1985), 187-193.
  12. J. C. Marrero, The local structure of trans-Sasakian manifolds, Ann. Mat. Mat. Pura Appl. 162 (1992), 77-86. https://doi.org/10.1007/BF01760000
  13. R. Prasad and V. Srivastava, Some Results on Trans-Sasakian Manifolds, Matematnykn Bechnk 65(3) (2013), 346-352.
  14. A.A. Shaikh, K.K. Baishya and S. Eyasmin, On D-Homothetic Deformation of Trans-Sasakian Structure, Demonstratio Mathematica 41(1) (2008), 171-188.
  15. S.S. Shukla and D.D. Singh, On (${\epsilon}$)-Trans-Sasakian Manifolds, Int. J. of Math. Analysis 49(4) (2010), 2401-2414.
  16. N. Tanaka, On non-degenerate real hypersurfaces, graded Lie Algebras and Cartan connections, Japan. J. Math. 2 (1976), 131-190. https://doi.org/10.4099/math1924.2.131
  17. S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314(1) (1989), 349-379. https://doi.org/10.1090/S0002-9947-1989-1000553-9
  18. S. M. Webster, Pseudohermitian structures on a real hypersurface, J. Differential Geom. 13 (1978), 25-41. https://doi.org/10.4310/jdg/1214434345
  19. S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36 DOI 10.1007/s10455-008-9147-3 (2009), 37-60.