Ray congruences that generate conformal foliations

Abstract

Given a Riemannian 3-manifold (M3, g0) endowed with a unit vector field U0 that is tangent to a conformal foliation, we require that the pair extend to a space-time \documentclass[12pt]{minimal}\begin{document}$({\mathcal M}, {\mathcal G})$\end{document}(M,G) endowed with a space-like unit vector field Ut in such a way that Ut simultaneously generates null geodesics and is tangent to a conformal foliation on space-like slices t = constant. The property that the foliation be conformal is intimately related to CR-geometry.