  We provide a detailed analysis of the electronic properties of graphene-like
materials with charge carriers living on a curved substrate, focusing in
particular on constant negative-curvature spacetime. An explicit
parametrization is also worked out in the remarkable case of Beltrami geometry,
with an analytic solution for the pseudoparticles modes living on the curved
bidimensional surface. We will then exploit the correspondent massless Dirac
description, to determine how it affects the sample local density of states.
