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

Sur la compl\'etude de certaines vari\'et\'es pseudo-riemanniennes localement sym\'etriques