CR-geometry and shearfree lorentzian geometry

Abstract

We study higher dimensional versions of shearfree null-congurences in conformal Lorentzian manifolds. We show that such structures induce a subconformal structure and a partially integrable almost CR-structure on the leaf space and we classify the Lorentzian metrics that induce the same subconformal structure. In the last section we survey some known applications of the correspondence between almost CR-structures and shearfree null-congurences in dimension 4.