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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 451
Twistor and Killing Spinors in Lorentzian Geometry Helga Baum
This paper is a survey about recent results concerning twistor and Killing spinors on Lorentzian manifolds based on lectures given at CIRM, Luminy, in June 1999, and at ESI, Wien, in October 1999. After some basic facts about twistor spinors we explain a relation between Lorentzian twistor spinors with lightlike Dirac current and the Fefferman spaces of strictly pseudoconvex spin manifolds which appear in CR-geometry. Secondly, we discuss the relation between twistor spinors with timelike Dirac current and Lorentzian Einstein Sasaki structures. Then, we indicate the local structure of all Lorentzian manifolds carrying real Killing spinors. In particular, we show a global Splitting Theorem for complete Lorentzian manifolds in the presence of Killing spinors. Finally, we review some facts about parallel spinors in Lorentzian geometry.
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