2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127717We study parabolic linear Weingarten surfaces in hyperbolic space $\rlopezh^3$. In particular, we classify two family of parabolic surfaces: surfaces with constant Gaussian curvature and surfaces that satisfy the relation $aκ_1+bκ_2=c$, where $κ_i$ are the principal curvatures, and $a,b$ and $c$ are constant.8 pages, 6 figures. This is the text of the talk presented in the International Congress on Pure and Applied Differential Geometry, PADGE 2007, 10-13 April, 2007. This is a brief of two preprints due to the author and that appear in the References sectionDifferential Geometry53text