Abstract
The techniques of spinorial geometry are used to classify solutions admitting Killing spinors in the theory of minimal anti-de Sitter N = 2, D = 4 supergravity, where the gauge kinetic term comes with the opposite sign. There are four classes of solutions. One class is described by metrics corresponding to gravitational waves propagating on AdS2 x H2. The second class of solution is a supersymmetric type III Kundt geometry corresponding to a special limiting case of the Killing spinor. The third class of solution corresponds to fibrations over a Lorentzian three dimensional manifold which has a Lorentzian Gauduchon-Tod structure. The fourth class of solution is a cosmological extension of a Majumdar-Papapetrou type solution, described by a function satisfying the wave equation on R2,1 .