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Non-commutative Integrability, Moment Map and Geodesic Flows

Alexey V. Bolsinov·Bozidar Jovanovic
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Abstract

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.

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Alexey V. Bolsinov, Bozidar Jovanovic. 2002-05-29. Non-commutative Integrability, Moment Map and Geodesic Flows. https://arxiv.org/abs/math-ph/0109031

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