Hamiltonian reductions of free particles under polar actions of compact Lie groups

Understand

Classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds are investigated.

• The reduced systems are described under the assumption that the underlying compact symmetry group acts in a polar manner in the sense that there exist regularly embedded, closed, connected submanifolds meeting all orbits orthogonally in the configuration space.
• Hyperpolar actions on Lie groups and on symmetric spaces lead to families of integrable systems of spin Calogero-Sutherland type.