The generalized Weierstrass system inducing surfaces of constant and nonconstant mean curvature in Euclidean three space

The generalized Weierstrass (GW) system is introduced and its correspondence with the associated two-dimensional nonlinear sigma model is reviewed. The method of symmetry reduction is systematically applied to derive several classes of invariant solutions for the GW system. The solutions can be used to induce constant mean curvature surfaces in Euclidean three space. Some properties of the system for the case of nonconstant mean curvature are introduced as well.