@article {
author = {Laleh, Abolghasem and Mir Mohamad Rezaii, Morteza and Ahangari, Fateme},
title = {Identification of Riemannian foliations on the
tangent bundle via SODE structure},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {38},
number = {3},
pages = {669-688},
year = {2012},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {The geometry of a system of second order differential equations is the geometry of a semispray, which is a globally defined vector field on TM. The metrizability of a given semispray is of special importance. In this paper, the metric associated with the semispray S is applied in order to study some types of foliations on the tangent bundle which are compatible with SODE structure. Indeed, sufficient conditions for the metric associated with the semispray S are obtained to extend to a bundle-like metric for the lifted foliation on TM. Thus, the lifted foliation converts to a Riemanian foliation on the tangent space which is adapted to the SODE structure. Particularly, the metrizability property of the semispray S is applied in order to induce SODE structure on transversals. Finally, some equivalent conditions are presented for the transversals to be totally geodesic.},
keywords = {Bundle-like metric,SODE,Semispray,Metrizability,Riemannian
Foliation},
url = {http://bims.iranjournals.ir/article_232.html},
eprint = {http://bims.iranjournals.ir/article_232_1c2426a4a61dca0c1d59277a7d46f0c0.pdf}
}