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Global Decomposition of a Lorentzian Manifold as a Generalized Robertson-walker Space

Generalized Robertson-Walker spaces constitute a quite important family in Lorentzian geometry, therefore it is an interesting question to know whether a Lorentzian manifold can be decomposed in such a way. The existence of a suitable vector field guaranties the local decomposition of the manifold, but the global one is a delicate topological problem. In this paper, we give conditions on the curvature which ensure a global decomposition and apply them to several situations where local decomposition appears naturally. Finally, we study the uniqueness question, obtaining that the de Sitter spaces are essentially the only complete Lorentzian manifolds with more than one decomposition. Moreover, we show that the Friedmann Cosmological Models admit an unique Generalized Robertson-Walker decomposition, even locally.