Non-commutative Integrability, Moment Map and Geodesic Flows
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The purpose of this paper is to discuss the relationship between commutative and non-commutative 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 non-commutative sense by means of polynomial integrals, and therefore, in classical commutative sense by means of $C^\infty$--smooth integrals.
19 pages, minor changes, to appear in Annals of Global Analysis and Geometry
19 pages, minor changes, to appear in Annals of Global Analysis and Geometry