Feuilletages totalement geodesiques, flots riemanniens et varietes de   Seifert
  We study totally geodesic codimension 1 smooth foliations on Lorentzian manifold. We are in particular interested by the relations between riemannian flows and geodesic foliations. We prove that, up to a 2-cover, any Seifert bundle admit such a foliation. 
Pierre Mounoud