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

Year 2018, Volume: 6 Issue: 1, 50 - 57, 27.04.2018

Hülya Bağdatlı Yılmaz

https://doi.org/10.36753/mathenot.421758

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.

Keywords

Almost contact metric manifold , Semi-symmetric non-metric connection , Curvature tensor

References

• [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.