Twistor spinors on Lorentzian symmetric spaces

An indecomposable Riemannian symmetric space which admits nontrivial twistor spinors has constant sectional curvature. Furthermore, each homogeneous Riemannian manifold with parallel spinors is at. In the present paper we solve the twistor equation on all indecomposable Lorentzian symmetric spaces explicitly. In particular, we show that there are-in contrast to the Riemannian case-indecom-posable Lorentzian symmetric spaces with twistor spinors, which have non-constant sectional curvature and non-at and non-Ricci at homogeneous Lorentzian man-ifolds with parallel spinors.