Abstract
We show that a class of solutions of minimal supergravity in ve dimensions is given by lifts of three{dimensional Einstein{Weyl structures of hyper-CR type. We characterise this class as most general near{horizon limits of supersymmetric solutions to the ve{ dimensional theory. In particular we deduce that a compact spatial section of a horizon can only be a Berger sphere, a product metric on S1 S2 or a at three-torus. We then consider the problem of reconstructing all supersymmetric solutions from a given near{horizon geometry. By exploiting the ellipticity of the linearised eld equations we demonstrate that the moduli space of transverse in nitesimal deformations of a near{ horizon geometry is nite{dimensional.