Abstract
We discuss the relation between solutions admitting Killing spinors of minimal supergravities in five dimensions and four dimensional complex geometries. In the ungauged case (vanishing cosmological constant _Lambda=0) the solutions are determined in terms of a hyper-Kahler base space; in the gauged case (_Lambda<0) the complex geometry is Kahler; in the de Sitter case (_Lambda>0) the complex geometry is hyper-Kahler with torsion (HKT). In the latter case some details of the derivation are given. The method for constructing explicit solutions is discussed in each case.