2134/17873 Alexey Bolsinov Alexey Bolsinov Integrable geodesic flows of Riemannian and sub-Riemannian metrics on Lie groups and homogeneous spaces Loughborough University 2015 untagged Mathematical Sciences not elsewhere classified 2015-06-16 10:00:27 Conference contribution https://repository.lboro.ac.uk/articles/conference_contribution/Integrable_geodesic_flows_of_Riemannian_and_sub-Riemannian_metrics_on_Lie_groups_and_homogeneous_spaces/9388061 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.