2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69053In this paper we study the flat (n+1)-spacetimes admitting a Cauchy surface diffeomorphic to a compact hyperbolic n-manifold. We show how to construct a canonical future complete one among all such spacetimes sharing the same holonomy. We study the geometry of such a spacetime in terms of its canonical cosmological time. In particular we study the asymptotic behaviour of the level surfaces of the cosmological time. The present work generalizes the case n=2 treated by Mess, taking from a work of Benedetti and Guadagnini the emphasis on the fundamental role played by the canonical cosmological time.59 pages, 9 figuresDifferential GeometryMathematical Physics53C50 (primary) 83C99 57M50 (secondary)text