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

Hülya Bağdatlı Yılmaz

doi:10.36753/mathenot.421758

EN

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

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.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Hülya Bağdatlı Yılmaz

Publication Date

April 27, 2018

Submission Date

November 19, 2017

Acceptance Date

-

Published in Issue

Year 2018 Volume: 6 Number: 1

DOI

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

IZ

https://izlik.org/JA27TH37PU

APA

Yılmaz, H. B. (2018). A Note on An Almost Contanct Metric Manifold with A Type of Semi-symmetric Non-metric Connection. Mathematical Sciences and Applications E-Notes, 6(1), 50-57. https://doi.org/10.36753/mathenot.421758

AMA

1.Yılmaz HB. A Note on An Almost Contanct Metric Manifold with A Type of Semi-symmetric Non-metric Connection. Math. Sci. Appl. E-Notes. 2018;6(1):50-57. doi:10.36753/mathenot.421758

Chicago

Yılmaz, Hülya Bağdatlı. 2018. “A Note on An Almost Contanct Metric Manifold With A Type of Semi-Symmetric Non-Metric Connection”. Mathematical Sciences and Applications E-Notes 6 (1): 50-57. https://doi.org/10.36753/mathenot.421758.

EndNote

Yılmaz HB (April 1, 2018) A Note on An Almost Contanct Metric Manifold with A Type of Semi-symmetric Non-metric Connection. Mathematical Sciences and Applications E-Notes 6 1 50–57.

IEEE

[1]H. B. Yılmaz, “A Note on An Almost Contanct Metric Manifold with A Type of Semi-symmetric Non-metric Connection”, Math. Sci. Appl. E-Notes, vol. 6, no. 1, pp. 50–57, Apr. 2018, doi: 10.36753/mathenot.421758.

ISNAD

Yılmaz, Hülya Bağdatlı. “A Note on An Almost Contanct Metric Manifold With A Type of Semi-Symmetric Non-Metric Connection”. Mathematical Sciences and Applications E-Notes 6/1 (April 1, 2018): 50-57. https://doi.org/10.36753/mathenot.421758.

JAMA

1.Yılmaz HB. A Note on An Almost Contanct Metric Manifold with A Type of Semi-symmetric Non-metric Connection. Math. Sci. Appl. E-Notes. 2018;6:50–57.

MLA

Yılmaz, Hülya Bağdatlı. “A Note on An Almost Contanct Metric Manifold With A Type of Semi-Symmetric Non-Metric Connection”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 1, Apr. 2018, pp. 50-57, doi:10.36753/mathenot.421758.

Vancouver

1.Hülya Bağdatlı Yılmaz. A Note on An Almost Contanct Metric Manifold with A Type of Semi-symmetric Non-metric Connection. Math. Sci. Appl. E-Notes. 2018 Apr. 1;6(1):50-7. doi:10.36753/mathenot.421758