Invariant metrics and Hamiltonian Systems
arXiv:math/0301332 · doi:10.1088/1742-6596/175/1/012012
Abstract
Via a non degenerate symmetric bilinear form we identify the coadjoint representation with a new representation and so we induce on the orbits a simplectic form. By considering Hamiltonian systems on the orbits we study some features of them and finally find commuting functions under the corresponding Lie-Poisson bracket
16 pages corrected typos, changed contents (Prop. 3.4 and Theorem in Section 3)