BOLSINOV, A.V., 2014. Integrable geodesic flows of Riemannian and sub-Riemannian metrics on Lie groups and homogeneous spaces. Scientific Semester “Geometry, Analysis and Dynamics on sub-Riemannian manifolds”: Thematic day on Riemannian and Sub-Riemannian Geometry on Lie Groups and Homogeneous Spaces, IHP, Paris, France, 13th-14th November 2014
We discuss general algebraic methods for constructing integrable geodesic flows of Riemannian and sub-Riemannian metrics on homogeneous spaces and Lie groups. Our approach is based on the concept of non-commutative integrability and the classical idea of dual Poisson algebras suggested by Sophus Lie.