Lorentzian twistor spinors and CR-geometry

Twistor Spinors on Lorentzian Manifolds, Cr-geometry and Feeerman Spaces

The paper deals with twistor spinors on Lorentzian manifolds. In particular , we explain a relation between a certain class of Lorentzian twistor spinors and the Feeerman spaces of strictly pseudoconvex spin manifolds which appear in CR-geometry. Let (M n;k ; g) be a n-dimensional smooth semi-Riemannian spin manifold of index k with the spinor bundle S. There are two conformally covariant diffe...

Twistor and Killing Spinors in Lorentzian Geometry

— This paper is a survey of 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...

A Note on Twistor Spinors with Zeros in Lorentzian Geometry

We show in this note that if a twistor spinor has a zero on a Lorentzian spin manifold M of arbitrary dimension then the twistor is almost everywhere on M locally conformally equivalent to a parallel spinor.

Twistor spinors on Lorentzian symmetric spaces

An indecomposable Riemannian symmetric space which admits nontrivial twistor spinors has constant sectional curvature. Furthermore, each homogeneous Riemannian manifold with parallel spinors is at. In the present paper we solve the twistor equation on all indecomposable Lorentzian symmetric spaces explicitly. In particular, we show that there are-in contrast to the Riemannian case-indecom-posab...

Zeros of Conformal Vector Fields and Twistor Spinors in Lorentzian Geometry