FROM 2D INTEGRABLE SYSTEMS TO SELF-DUAL GRAVITY

We explain how to construct solutions to the self-dual Einstein vacuum equations from solutions of various two-dimensional (2D) integrable s ystems by exploiting the fact that the Lax formulations of both system s can be embedded in that of the self-dual Yang-Mills equations. We il lustrate this by constructing explicit self-dual vacuum metrics on R-2 x Sigma, where Sigma is a homogeneous space for a real subgroup of SL (2, C) associated with the 2D system.