2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63102The purpose of this note is to make some connection between the sub-Riemannian geometry on Carnot-Caratheodory groups and symplectic geometry. We shall concentrate here on the Heisenberg group, although it is transparent that almost everything can be done on a general Carnot-Caratheodory group. Such generalisations will be the subject of a forthcoming note.Symplectic GeometryMetric Geometry53C17, 53D05Symplectic, Hofer and sub-Riemannian geometrytext