2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78501The Landau-Lifshitz equation is derived as the reduction of a geodesic flow on the group of maps into the rotation group. Passing the symmetries of spatial isotropy to the reduced space is an example of semidirect product reduction by stages.12 pages. A significant topological oversight was corrected. To appear Lett. Math. PhysSymplectic GeometryMathematical PhysicsDifferential Geometrytext