Noncommutative Integrability, Moment Map and Geodesic Flows

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...

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Bibliographic Details
Published in:Annals of global analysis and geometry 2003-06, Vol.23 (4), p.305
Main Authors: Bolsinov, Alexey V, Jovanovic, Bozidar
Format: Article
Language:English
Subjects:
Algebra
Commuting
Geometry
Integrals
Lie groups
Mathematical models
Studies
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Summary: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 ofC[infinity]-smooth integrals. [PUBLICATION ABSTRACT]
ISSN:0232-704X
1572-9060
DOI:10.1023/A:1023023300665