2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71545Suppose that N is a geometrically finite orientable hyperbolic 3-manifold. Let P(N,C) be the space of all geometrically finite hyperbolic structures on N whose convex core is bent along a set C of simple closed curves. We prove that the map which associates to each structure in P(N,C) the lengths of the curves in the bending locus C is one-to-one. If C is maximal, the traces of the curves in C are local parameters for the representation space R(N).46 pages, 3 figures; v2: corrections and improved expositionGeometric Topology30F40text