|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Noncommutative Integrability, Moment Map and Geodesic Flows||Journal:||Annals of Global Analysis and Geometry||Volume:||23||Issue:||4||First page:||305||Last page:||322||Issue Date:||1-Jan-2003||Rank:||M22||ISSN:||0232-704X||DOI:||10.1023/A:1023023300665||Abstract:||
The purpose of this paper is to discuss the relationship between commutative and noncommutative integrability of Hamiltonian systems and to construct new examples of integrable geodesic flows on Riemannian manifolds. In particular, we prove that the geodesic flow of the bi-invariant metric on any bi-quotient of a compact Lie group is integrable in the noncommutative sense by means of polynomial integrals, and therefore, in the classical commutative sense by means of C∞-smooth integrals.
|Keywords:||Geodesic flows | Hamiltonian action of a Lie group | Integrable Hamiltonian systems | Noncommutative integrability||Publisher:||Springer Link||Project:||Russian Fund for Fundamental Research (grants 02-01-00998 and 00-15-99272)
Serbian Ministry of Science and Technology, Project 1643 (Geometry and Topology of Manifolds and Integrable Dynamical Systems)
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