Einstein-Weyl structures and de Sitter supergravity

The geometric structure of the null solutions of de Sitter D = 5 gauged supergravity coupled to vector multiplets is investigated. These solutions are Kundt metrics, constructed from a one-parameter family of three-dimensional Gauduchon-Tod base spaces. We give examples, including the near-horizon geometries previously found in Gutowski and Sabra (2011 J. High Energy Phys. JHEP05(2011)020). In addition, two special cases are considered in detail. In the first case, we consider solutions for which the Gauduchon-Tod base space is the Berger sphere. In the second case, we take the null 1-form Killing spinor bilinear to be recurrent, so that the holonomy of the Levi-Civita connection is contained in Sim(3). (paper)