2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61817Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions we define the notions of generalized pseudo-Riemannian metric, generalized connection and generalized curvature tensor. We prove a ``Fundamental Lemma of (pseudo-)Riemannian geometry'' in this setting and define the notion of geodesics of a generalized metric. Finally, we present applications of the resulting theory to general relativity.23 pages, Latex, final formFunctional AnalysisGeneral Relativity and Quantum CosmologyDifferential GeometryPrimary: 46F30; secondary: 46T30, 46F10, 83C05text