2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56595Wave maps (i.e. nonlinear sigma models) with torsion are considered in 2+1 dimensions. Global existence of smooth solutions to the Cauchy problem is proven for certain reductions under a translation group action: invariant wave maps into general targets, and equivariant wave maps into Lie group targets. In the case of Lie group targets (i.e. chiral models), a geometrical characterization of invariant and equivariant wave maps is given in terms of a formulation using frames.37 pages, LaTex, no figuresMathematical PhysicsAnalysis of PDEs35Q, 35L70text