Integrable geodesic flows of Riemannian and sub-Riemannian metrics on Lie groups and homogeneous spaces

2015-06-16T10:00:27Z (GMT) by Alexey V. Bolsinov
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.