Abstract
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.
Citation
Ken Yokumoto. "Examples of Lorentzian geodesible foliations of closed three-manifolds having Heegaard splittings of genus one." Tohoku Math. J. (2) 56 (3) 423 - 443, 2004. https://doi.org/10.2748/tmj/1113246677
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