Authors: Bolsinov, Alexey
Jovanović, Božidar 
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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