Noncommutative Integrability,Moment Map and Geodesic Flows |
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Authors: | Bolsinov,Alexey V.,Jovanović , Bož idar |
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Affiliation: | (1) Department of Mechanics and Mathematics, Moscow State University, 119899 Moscow, Russia;(2) Matematiki Institut, SANU, Kneza Mihaila 35, 11000 Beograd, Serbia, Yugoslavia |
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Abstract: | The purpose of this paper is to discuss the relationship betweencommutative and noncommutative integrability of Hamiltonian systemsand to construct new examples of integrable geodesic flows onRiemannian manifolds. In particular, we prove that the geodesic flowof the bi-invariant metric on any bi-quotient of a compact Lie group isintegrable in the noncommutative sense by means of polynomial integrals, andtherefore, in the classical commutative sense by means ofC-smooth integrals. |
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Keywords: | integrable Hamiltonian systems geodesic flows Hamiltonian action of a Lie group noncommutative integrability |
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