Paper detail

Sur la complétude de certaines variétés pseudo-riemanniennes localement symétriques

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.