2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165163We characterize isometric actions on compact Kaehler manifolds admitting a Lagrangian orbit, describing under which condition the Lagrangian orbit is unique. We furthermore give the complete classification of simple groups acting on the complex projective space with a Lagrangian orbit, and we give the explicit list of these orbits.17 pages. Minor modifications have been made: Proposition 5 is now correctly quoted, Corollary 2 and 3 are addedDifferential GeometrySymplectic Geometry32J27; 53D20text