2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58742We find obstructions to the existence of Einstein metrics of non-negative sectional curvature on a smooth closed simply connected manifold of any dimension. The results are achieved by combining the classical Morse theory of the loop space with a new upper bound for the topological entropy of the geodesic flow in terms of the curvature tensor.13 pagesDifferential GeometryDynamical Systems53C25text