Twistor spinors on Lorentzian symmetric spaces

An indecomposable Riemannian symmetric space which admits non-trivial twist er spinors has constant sectional curvature. Furthermore. each homogeneous Riemannian manifold with parallel spinors is hat. In the present paper we s olve the twister equation on all indecomposable Lorentzian symmetric spaces explicitly. In particular, we show that there are - in contrast to the Rie mannian case - indecomposable Lorentzian symmetric spaces with twister spin ors, which have non-constant sectional curvature and non-flat and non-Ricci hat homogeneous Lorentzian manifolds with parallel spinors. (C) 2000 Elsev ier Science B.V. All rights reserved.