Abstract
We study Riemannian submersions from a Riemannian manifold endowed with a semi-symmetric non-metric connection onto a Riemannian manifold. We give an example and investigate O'Neill's tensor fields, obtain derivatives of those tensor fields and compare curvatures of the total manifold, the base manifold and the fibres by computing curvatures.
Keywords
Riemannian submersion semi-symmetric non-metric connection O'Neill tensors vertical distribution
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), no 6, 399-409.
- [2] Altafini C., Redundant robotic chains on Riemannian submersions IEEE Transactions on Robotics and Automation, 2004, 20(2), 335-340
- [3] Falcitelli, M., Ianus, S., Pastore, A. M. Riemannian Submersions and Related Topics, World Scientific, 2004
- [4] Friedmann, A. and Schouten, J.A., U¨ ber die Geometrie der halbsymmetrischen U¨ bertragung, Math. Zeitschr., 21(1924), 211-223.
- [5] Gray, A., Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16 1967 715–737.
- [6] Hayden, H. A., Subspaces of a space with torsion, Proc. London Math. Soc. 34(1), (1932), 27-50.
- [7] G¨und¨uzalp, Y., Riemann submersiyonlarının geometrisi ¨uzerine, Y¨uksek lisans tezi, Malatya, 2007.
- [8] O’Neill, B., The fundamental equations of a submersion, Michigan Math. J. 13(1966), 459-469.
- [9] S¸ ahin, B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications (Elsevier, Academic Press, Massachusetts, Cambridge, 2017).
- [10] Yano, K., On semi-symmetric metric connection. Rev. Roumaine Math. Pures Appl. 15 1970 1579-1586.
- [11] Yücesan, A., Yas¸ar, E., Semi-Riemannian submanifolds of a semi-Riemannian manifold with a semi-symmetric non-metric connection. Commun. Korean Math. Soc. 27(4), (2012), 781-793
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), no 6, 399-409.
- [2] Altafini C., Redundant robotic chains on Riemannian submersions IEEE Transactions on Robotics and Automation, 2004, 20(2), 335-340
- [3] Falcitelli, M., Ianus, S., Pastore, A. M. Riemannian Submersions and Related Topics, World Scientific, 2004
- [4] Friedmann, A. and Schouten, J.A., U¨ ber die Geometrie der halbsymmetrischen U¨ bertragung, Math. Zeitschr., 21(1924), 211-223.
- [5] Gray, A., Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16 1967 715–737.
- [6] Hayden, H. A., Subspaces of a space with torsion, Proc. London Math. Soc. 34(1), (1932), 27-50.
- [7] G¨und¨uzalp, Y., Riemann submersiyonlarının geometrisi ¨uzerine, Y¨uksek lisans tezi, Malatya, 2007.
- [8] O’Neill, B., The fundamental equations of a submersion, Michigan Math. J. 13(1966), 459-469.
- [9] S¸ ahin, B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications (Elsevier, Academic Press, Massachusetts, Cambridge, 2017).
- [10] Yano, K., On semi-symmetric metric connection. Rev. Roumaine Math. Pures Appl. 15 1970 1579-1586.
- [11] Yücesan, A., Yas¸ar, E., Semi-Riemannian submanifolds of a semi-Riemannian manifold with a semi-symmetric non-metric connection. Commun. Korean Math. Soc. 27(4), (2012), 781-793
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | April 15, 2018 |
| Submission Date | July 25, 2017 |
| Acceptance Date | February 1, 2018 |
| Published in Issue | Year 2018 Volume: 6 Issue: 1 |
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