N=2 String Geometry and the Heavenly Equations

Abstract

In this paper we survey some of the relations between Plebanski description of self-dual gravity through the heavenly equations and the physics (and mathematics) of N=2 Strings. In particular we focus on the correspondence between the infinite hierarchy in the ground ring structure of BRST operators and its associated Boyer-Plebanski construction of infinite conserved quantities in self-dual gravity. We comment on ``Mirror Symmetry'' in these models and the large-N duality between topological N=4 gauge theories in two dimensions and topological gravity in four dimensions. Finally D-branes in this context are briefly outlined.