A Note on An Almost Contanct Metric Manifold with A Type of Semi-symmetric Non-metric Connection (original) (raw)

Abstract

In this paper, we focus on an almost contact metric manifold admitting a type of semi-symmetric nonmetric connection. We find the expression for the curvature tensor of such a manifold. Furhermore, we study the properties of the curvature tensor and the projective curvature tensor.

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References (19)

  1. Agashe, N. S. and Chafle, M. R., A semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math 23 (1992), 399-409.
  2. Blair, D. E., The theory of quasi-Sasakian structures J. Diff. Geom. 1 (1967), 331-345.
  3. Blair, D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Math., 0509, Springer-Verlag, Berlin 1976.
  4. Chaubey, S. K., On semi symmetric non-metric connection, Prog. of Math., 41-42(2007), 11-20.
  5. Chaubey, S. K. and Ojha, R. H., On semi symmetric non-metric connection and quarter symmetric connections, Tensor N. S., 70 (2008),No:2, 202-213.
  6. Chaubey, S. K. and Ojha, R. H., On semi symmetric non-metric connection, Filomat, 25:4(2011) , 19-27.
  7. De, U. C. and Biswas, S. C., On a type of semi symmetric non-metric connection on a Riemannian manifold, Pub. De L'institut Math. Nouvelle serie tome 61, 1997, 90-96.
  8. Friedmann, A. and Schouten, J. A., Über die Geometric der holbsymmetrischen Übertragurgen, Math. Z., 21(1924), 211-233.
  9. Gray, J., Some global properties of contact structures, Ann. of Math., 69(1959), 421-450.
  10. Hayden, H. A., Subspaces of space with torsion, Proc. London Math. Soc., 34(1932), 27-50.
  11. Janssens, D. and Vanhecke, L., Almost contact structures and curvature tensors, Kodai Math. J., 4 (1981), 1-27.
  12. Liang,Y., On semi-symmetric recurrent metric connection, Tensor N. S. 55 (1994), 107-102.
  13. Oubina, J., New classes of almost contact metric structures, Publicationes Mathematicae, 32 (1985), 187-193.
  14. Pravonovic, M., On pseudo symmetric semi-symmetric connection, Pub. De L'Institu Math., Nouvelle Serie, 18(32) (1975), 157-164.
  15. Sasaki, S., On diff. manifolds with certain structures which are closely related to almost contact structure I, Tohoku Math. J., 12(1960), 459-476.
  16. Sengupta, J., De, U. C. and Binh, T. Q., On a type of semi symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math.,31(12) (2000),1659-1670.
  17. Yano, K., On semi-symmetric metric connections, Revue Roumania De Math. Pures Appl. 15 (1970), 1579-1586.
  18. Yılmaz, H. B., On weakly symmetric manifolds with a type of semi-symmetric non-metric connection, Ann. Polonici Math., 102.3 (2011),301-308. Affiliation HÜLYA BA GDATLI YILMAZ ADDRESS: Marmara University, Dept. of Sciences and Letters, 34722, Istanbul-Turkey.
  19. E-MAIL: hbagdatli@marmara.edu.tr ORCID ID: 0000 -0003 -2568 -7577