Examples of Lorentzian geodesible foliations of closed three-manifolds having Heegaard splittings of genus one

摘要

We construct codimension-one, Lorentzian geodesible foliations of closed three-manifolds having Heegaard splittings of genus one. We prove that all the inner leaves of a Reeb component of a codimension-one, totally geodesic foliation of a Lorentzian three-manifold are spacelike, and the boundary leaf of a Reeb component is lightlike.