The geodesic flow on nilmanifolds
Differential Geometry
2019-07-24 v1 Dynamical Systems
Abstract
In this paper we study the geodesic flow on nilmanifolds equipped with a left-invariant metric. We write the underlying definitions and find general formulas for the Poisson involution. As an example we develop the Heisenberg Lie group equipped with its canonical metric. We prove that a family of first integrals giving the complete integrability can be read off at the Lie algebra of the isometry group. We also explain the complete integrability on compact quotients and for any invariant metric.
Cite
@article{arxiv.1508.05286,
title = {The geodesic flow on nilmanifolds},
author = {Alejandro Kocsard and Gabriela P. Ovando and Silvio Reggiani},
journal= {arXiv preprint arXiv:1508.05286},
year = {2019}
}
Comments
24 pages