  We prove that some symetric semi-riemannian manifolds do not admit a proper
domain which is divisible by the action of a discrete group of isometries. In
other words, if a closed semi-riemannian manifold is locally isometric to such
a model, and if its developing map is injective, then the manifold is actually
geodesically complete, and therefore isometric to a quotient of the whole model
space. Those results extend, under additional hypothesis (the injectivity of
the developing map), the theorems of Carriere and Klingler stating that closed
lorentz manifolds of constant curvature are geodesically complete.
