Bryant, RBourguinon, JPBranson, THijazi, O2016-08-2520002-85629-094-9https://hdl.handle.net/10161/12694I discuss geometry and normal forms for pseudo-Riemannian metrics with parallel spinor fields in some interesting dimensions. I also discuss the interaction of these conditions for parallel spinor fields with the condition that the Ricci tensor vanish (which, for pseudo-Riemannian manifolds, is not an automatic consequence of the existence of a nontrivial parallel spinor field).spinorsRicci curvatureBook section