  We describe up to finite coverings causal flat affine complete Lorentzian
manifolds such that the past and the future of any point are closed near this
point. We say that these manifolds are strictly causal. In particular, we prove
that their fundamental groups are virtually abelian. In dimension 4, there is
only one, up to a scaling factor, strictly causal manifold which is not
globally hyperbolic. For a generic point of this manifold, either the past or
the future is not closed and contains a lightlike straight line.

Metric Geometry;Differential Geometry