Parabolic surfaces in hyperbolic space with constant curvature

Abstract

We 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 $a{\kappa }_1+b{\kappa }_2=c$, where ${\kappa }_i$ 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 section