2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59982We study Hamiltonian stationary Lagrangian surfaces in C^2, i.e. Lagrangian surfaces in C^2 which are stationary points of the area functional under smooth Hamiltonian variations. Using loop groups, we propose a formulation of the equation as a completely integrable system. We construct a Weierstrass type representation and produce all tori through either the integrable systems machinery or more direct arguments.3 figuresDifferential Geometry53C42 (Primary) 58E20, 58F07 (Secondary)text