Five Dimensional Minimal Supergravities and Four Dimensional Complex Geometries
arXiv:0901.4066 · doi:10.1063/1.3141231
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 Λ=0) the solutions are determined in terms of a hyper-Kahler base space; in the gauged case (Λ<0) the complex geometry is Kahler; in the de Sitter case (Λ>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.
8 pages. Contribution to the Proceedings of the Spanish Relativity Meeting 2008 in Salamanca, Spain
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