b-Completion of pseudo-Hermitian manifolds

International audienceWe study the interrelation among pseudo-Hermitian and Lorentzian geometry as prompted by the existence of the Fefferman metric. Specifically for any nondegenerate Cauchy-Riemann manifold M we build its b-boundary [$\dot{M}$]. This arises as a S1 quotient of the b-boundary of the (total space of the canonical circle bundle over M endowed with the) Fefferman metric. Points of [$\dot{M}$] are shown to be endpoints of b-incomplete curves. A class of inextensible integral curves of the Reeb vector on a pseudo-Einstein manifold is shown to have an endpoint on the b-boundary provided that the horizontal gradient of the pseudo-Hermitian scalar curvature satisfies an appropriate boundedness condition