  In 1872 G. Darboux defined a family of curves on surfaces of R^3 which are
preserved by the action of the Mobius group and share many properties with
geodesics. Here we characterize these curves under the view point of Lorentz
geometry and prove some general properties and make them explicit them on
simple surfaces, retrieving results of Pell (1900) and Santalo (1941).
