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Year 2018, , 50 - 57, 27.04.2018
https://doi.org/10.36753/mathenot.421758

Abstract

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.

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

Year 2018, , 50 - 57, 27.04.2018
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.

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.
There are 17 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Hülya Bağdatlı Yılmaz

Publication Date April 27, 2018
Submission Date November 19, 2017
Published in Issue Year 2018

Cite

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 Yılmaz HB. A Note on An Almost Contanct Metric Manifold with A Type of Semi-symmetric Non-metric Connection. Math. Sci. Appl. E-Notes. April 2018;6(1):50-57. doi:10.36753/mathenot.421758
Chicago 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, no. 1 (April 2018): 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 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, 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 2018), 50-57. https://doi.org/10.36753/mathenot.421758.
JAMA 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, 2018, pp. 50-57, doi:10.36753/mathenot.421758.
Vancouver 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):50-7.

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