Neutral surfaces in neutral four-spaces

Properties of the Gauss map of neutral surfaces are studied. Special attention is given to surfaces of parallel, or zero, mean curvature. Bilagrangian structures are defined and used in ways analogous to the use of complex structures in the Riemannian case. The nonsimplicity of the structure group SO(2,2) is used to factor the Gauss map and to construct analogs of the twistor space, called in this context reflector space.