Parallel spinors on pseudo-Riemannian spincspinc manifolds

We describe, by their holonomy groups, all simply connected irreducible non-locally symmetric pseudo-Riemannian spincspinc manifolds which admit parallel spinors. So we generalize the Riemannian spincspinc case [A. Moroianu, Parallel and killing spinors on spincspinc manifolds, Commun. Math. Phys. 187 (1997) 417–427] and the pseudo-Riemannian spin one [1].