Riemannian submersions endowed with a semi-symmetric non-metric connection
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
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.
Details
Primary Language
English
Subjects
Engineering
Journal Section
Research Article
Authors
Mehmet Akif Akyol
*
Bingöl University, Faculty of Art and Science Department of Mathematics, Bingol, Turkey
Türkiye
Selahattin Beyendi
Türkiye
Publication Date
April 15, 2018
Submission Date
July 25, 2017
Acceptance Date
February 1, 2018
Published in Issue
Year 2018 Volume: 6 Number: 1
