2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159125Spacetimes have conventionally been described by a global Lorentzian metric on a differentiable four-manifold. Herein we explore the possibility of spacetimes defined by a connection, which is locally but not globally Levi-Civita. The general method of obtaining such connections is presented for the non-degenerate case followed by an example that modifies the Robertson-Walker spacetimes for flat spacelike hypersurfaces.16 pagesMathematical Physicstext