Integrable geodesic flows of non-holonomic metrics
dg-ga
2008-02-03 v1 Differential Geometry
Abstract
Normal geodesic flows flows of Carnot-Caratheodory are discussed from the point of view of the theory of Hamiltonian systems. The geodesic flows corresponding to left-invariant metrics and left- and -right-invariant rank 2 distributions on the three-dimensional Heisenberg group are analysed as integrable systems. The flows corresponding to left-invariant metrics and left-invariant distributions on Lie groups are reduced to Euler equations on Lie groups. Relation of these constructions to problems of analytical mechanics is discussed.
Keywords
Cite
@article{arxiv.dg-ga/9610012,
title = {Integrable geodesic flows of non-holonomic metrics},
author = {I. A. Taimanov},
journal= {arXiv preprint arXiv:dg-ga/9610012},
year = {2008}
}
Comments
15 pages, LaTeX