2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112807Using a four points inequality for the boundary of CAT(-1)-spaces, we study the relation between Gromov hyperbolic spaces and CAT(-1)-spaces.This updated version includes some further observations concerning the Ptolemy inequality. Some proofs have been improved and several typos have been correctedMetric Geometry53C20text