Integrable geodesic flows on homogeneous spaces
- 1 December 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 1 (4) , 495-517
- https://doi.org/10.1017/s0143385700001401
Abstract
A method is exposed which allows the construction of families of first integrals in involution for Hamiltonian systems which are invariant under the Hamiltonian action of a Lie group G. This is applied to invariant Hamiltonian systems on the tangent bundles of certain homogeneous spaces M = G/K. It is proved, for example, that every such invariant Hamiltonian system is completely integrable if M is a real or complex Grassmannian manifold or SU(n + 1)/SO(n + 1) or a distance sphere in ℂPn+1. In particular, the geodesic flows of these homogeneous spaces are integrable.Keywords
This publication has 5 references indexed in Scilit:
- The moment map and collective motionAnnals of Physics, 1980
- Mathematical Methods of Classical MechanicsPublished by Springer Nature ,1978
- The jacobi equation on naturally reductive compact Riemannian homogeneous spacesCommentarii Mathematici Helvetici, 1977
- Fundamental Solutions of Invariant Differential Operators on Symmetric SpacesAmerican Journal of Mathematics, 1964
- Invariants of Finite Reflection GroupsCanadian Journal of Mathematics, 1960