Tohoku Mathematical Journal
2004

September
SECOND SERIES VOL. 56, NO. 3

Tohoku Math. J.
56 (2004), 423-443

Title EXAMPLES OF LORENTZIAN GEODESIBLE FOLIATIONS OF CLOSED THREE-MANIFOLDS HAVING HEEGAARD SPLITTINGS OF GENUS ONE

Author Ken Yokumoto

(Received February 5, 2003, revised August 27, 2003)
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.

2000 Mathematics Subject Classification. Primary 57R30; Secondary 53C50.

Key words and phrases. Lorentzian manifolds, totally geodesic foliations.

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