Réalisation du flot géodesique sur le groupe SO(n) comme flot sur des orbites de Kotant-Kirillov/Realization of geodesic flow on the group SO(n) as a flow on Kostant-Kirillov orbits

Abstract

The aim of this paper is to realize the geodesic flow on the group SO(n) as a flow on the Kostant-Kirillov orbits. We study the adjoint and coadjoint orbits of a Lie group with an application in the case of the orthogonal special group SO(n). We will see how to explicitly determine a symplectic structure in the orbit of the coadjoint representation of a Lie group. Special attention is given to the groups SO(3) and SO(4).

Keywords

• Symplectic manifolds
• Symplectic structures