A surface in hyperbolic space H 3 invariant by a group of parabolic isometries is called a parabolic surface. In this paper we investigate parabolic surfaces of H 3 that satisfy a linear Weingarten relation of the form aκ1 + bκ2 = c or aH + bK = c, where a, b, c ∈ R and, as usual, κi are the principal curvatures, H is the mean curvature and K is de Gaussian curvature. We classify all parabolic ...