Parabolic surfaces in hyperbolic space with constant curvature

We study parabolic linear Weingarten surfaces in hyperbolic space ${\text{rlopezh}}^3$. In particular, we classify two family of parabolic surfaces: surfaces with constant Gaussian curvature and surfaces that satisfy the relation $a{\kappa }_1+b{\kappa }_2=c$, where ${\kappa }_i$ are the principal curvatures, and $a,b$ and $c$ are constant.