  A Sim(n-1,1) affine manifold is an affine manifold whose linear holonomy is
contained in the similarity lorentzian group but not in the lorentzian group.
The class of similarity lorentzian affine manifolds is a small part in the nice
class of conformally lorentzian flat manifolds. In this paper we show that a
compact Sim(n-1,1) affine manifold is incomplete. We characterize the universal
cover of radiant compact Sim(n-1,1) affine manifolds whose developing map is
injective. Let q be the quadratic form which define the Sim(n-1,1) structure,
using riemannian foliation theory, we classify compact radiant Sim(n-1,1)
affine manifolds M such that D(M') the image of the universal cover M' of M by
the developing map D is contained in the upper cone defined q
