Killing spinors on Lorentzian manifolds (Q1867207)

The author studies Killing spinors on Lorentzian spin manifolds and, in particular, proves that 1) there are non-Einstein Lorentzian manifolds admitting imaginary Killing spinors (notice that for a Riemannian spin manifold the existence of a nontrivial Killing spinor implies that the manifold is Einstein); 2) a Lorentzian manifold admitting a nontrivial real Killing spinor locally looks as a codimension warped product whose fiber is either a Riemannian manifold with real, or imaginary, or parallel Killing spinor or a Lorentzian manifold with a real Killing spinor. He derives from the second statement that a Lorentzian manifold with a real Killing spinor is an Einstein manifold.