Riemannian submersions endowed with a semi-symmetric non-metric connection

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,

PDF

___

[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

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

Arşiv