Abstract
This paper is a survey of recent results about conformal Killing spinors in Lorentzian geometry based on a lecture given during the Summer Program Symmetries and Overdetermined Systems of Partial Differential Equations at IMA, Minnesota, 17.07.06 – 04.08.06. In particular, we will focus on a special class of geometries admitting conformai Killing spinors — on Brinkmann spaces with parallel spinors. We will discuss their holonomy groups and the global realizability as globally hyperbolic spaces with complete Cauchy surfaces.Key wordsLorentzian manifoldspinorconformal Killing spinortwistor spinortwistor equationBrinkmann spaceholonomy groupparallel spinorglobally hyperbolic manifoldAMS(MOS) subject classification53C2953C2753B5053C15
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