NONLINEAR SIGMA-MODELS ON SPHERES AND TODA SYSTEMS

Non-linear a-models on spheres (or harmonic maps in spheres) are inves tigated. Two classes of solutions characterized by vanishing of certai n differentials are studied. It is shown that for these classes the co rresponding non-linear field equations reduce to a real version of two -dimensional Toda systems (non-periodic for the first class and period ic for the second one). The discussed setting serves as a unifying sch eme for many particular results.