Non-commutative Integrability, Moment Map and Geodesic Flows

Details Non-commutative Integrability, Moment Map and Geodesic Flows Non-commutative Integrability, Moment Map and Geodesic Flows

2001-09-27

arxiv.org/abs/math-ph/0109031v2

Annals of Global Analysis and Geometry, 23 (4): 305-322, 2003

Physics

Mathematical Physics

19 pages, minor changes, to appear in Annals of Global Analysis and Geometry

Scientific paper

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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