2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164605Conformally compact asymptotically hyperbolic metrics have been intensively studied. The goal of this note is to understand what intrinsic conditions on a complete Riemannian manifold (M,g) will ensure that g is asymptotically hyperbolic in this sense. We use the geodesic compactification by asymptotic geodesic rays to compactify M and appropriate curvature decay conditions to study the regularity of the conformal compactification. We also present an interesting example that shows our conclusion is nearly optimal for our assumptions.18 pages; correction to Theorem 1Differential Geometry53C21text