Riemannian Submersions with Quarter- Symmetric Non-Metric Connection

Year 2021, Volume: 6 Issue: 1, 1 - 8, 30.04.2021

Hakan Demir Ramazan Sarı

https://doi.org/10.30931/jetas.910481

Cited By: 1

Abstract

In this paper, we study Riemannian submersions from a Riemannian manifold endowed with a quarter-symmetric non-metric connection onto a Riemannian manifold. We investigate O’Neill’s tensor fields for quarter-symmetric non-metric connection and derive the covariant derivative of O’Neill’s tensor fields. We obtain derivatives of those tensor fields and compare curvatures of the total manifold, the base manifold, and the fibers by computing curvatures.

Keywords

Riemannian submersion, quarter symmetric connection, O'Neill tensors

References

• [1] Friedmann, A., Schouten, J.A., “Über die Geometrie der halbsymmetrischen Ü bertragung”, Math. Zeitschr. 21 (1924) : 211-223.
• [2] Hayden, H.A., “Subspaces of a space with torsion”, Proc. London Math. Soc. 34(1) (1932) : 27-50.
• [3] Yano,K., “On semi symmetric metric connection”, Rev. Roumaine Math. Pures Appl.15 (1970), 1579-1586.
• [4] Ayar, G., Demirhan, D., “Ricci solition on nearly Kenmotsu manifolds with semi-symmetric metric connection”, Journal of Engineering Technology and Applied Sciences 4(3) (2019) : 131- 140.
• [5] Altın, M., “Projective Curvature N(k) Contact metric manifold admitting semi-symetric non-metric connection”, Fundamental Journal of Mathematics and Applications 3(2) (2020) : 94-100.
• [6] Chaubey, S. K., Ojha, R.H., “On semi-symmetric non-metric and quarter symmetric metric connections”, Tensor N. S. 70(2) (2008) : 202-213.
• [7] Golab, S., “On semi- symmetric metric and quarter symmetric linear connections”, Tensor 29, (1975), 249-254.
• [8] Dubey, A. K. Ojha, R. H. and Chaubey, S. K., “Some properties of quarter symmetric non-metric connection in a Kahler manifold”, Int. J. Contemp. Math.Sciences, 5(20), (2010), 1001-1007.
• [9] Mishra, R. S. and Pandey, S. N., “On quarter symmetric metric F-connections”, Tensor N. S., 34, (1980), 1-7.
• [10] Rastogi, S. C., “On quarter-symmetric metric connection”, C. R. Acad. Bulg. Sci. 31(8) (1978) : 811-814.
• [11] Sarı,R. Akyol,M.A. Aksoy,E., “Some curvature properties of an S-manifold with a quarter symmetric non metric connection”, International Journal of Applied Mathematics and Statistic 56(3) (2017) : 93-102.
• [12] O’Neill, B., “The fundamental equations of a submersion”, Michigan Math. J., 13, (1966), 459-469.
• [13] Gray, A., “Pseudo Riemannian almost product manifold and submersions”, J. Math Metch. 16 (1967) : 715-737.
• [14] Akyol M.A., Beyendi S., “Riemannian submersions endowed with a semi-symmetric nonmetric connection”, Konuralp Journal of Mathematics 6(1) (2018) : 188-193.