Integrable magnetic geodesic flows on Lie groups
Mathematical Physics
2011-11-04 v1 math.MP
Abstract
Right-invariant geodesic flows on manifolds of Lie groups associated with 2-cocycles of corresponding Lie algebras are discussed. Algebra of integrals of motion for magnetic geodesic flows is considered and necessary and sufficient condition of integrability in quadratures is formulated. Canonic forms for 2-cocycles of all 4-dimensional Lie algebras are given and integrable cases among them are separated.
Cite
@article{arxiv.1111.0726,
title = {Integrable magnetic geodesic flows on Lie groups},
author = {Alexey A. Magazev and Igor V. Shirokov and Yuriy Y. Yurevich},
journal= {arXiv preprint arXiv:1111.0726},
year = {2011}
}
Comments
16 pages