Christoph Bohle
Killing Spinors on Lorentzian Manifolds
(310K, postscript)

ABSTRACT.  The aim of this paper is to describe some results concerning the geometry 
of Lorentzian manifolds admitting Killing spinors. We prove that there are 
imaginary Killing spinors on simply connected Lorentzian Einstein--Sasaki 
manifolds. In the Riemannian case, an odd--dimensional complete 
simply connected manifold (of dimension $n\neq7$) is Einstein--Sasaki if and 
only if it admits a non-trivial Killing spinor to $\lambda = \pm\frac12$. 
The analogous result does not hold in the Lorentzian case. We give 
an example of a non--Einstein Lorentzian manifold admitting an imaginary 
Killing spinor. A Lorentzian manifold admitting a real Killing spinor is at 
least locally a codimension one warped product with a special warping 
function. The fiber of the warped product is either a Riemannian manifold 
with a real or imaginary Killing spinor or with a parallel spinor, or it again 
is a Lorentzian manifold with a real Killing spinor. Conversely, all warped 
products of that form admit real Killing spinors.