Global existence for wave maps with torsion

Wave maps (i.e. nonlinear sigma models) with torsion are considered in 2+1 dimensions. Global existence of smooth solutions to the Cauchy problem is p roven for certain reductions under a translation group action: invariant wa ve maps into general targets, and equivariant wave maps into Lie group targ ets. In the case of Lie group targets (i.e. chiral models), a geometrical c haracterization of invariant and equivariant wave maps is given in terms of a formulation using frames.