Dynamical behavior of Darboux curves

الأصل · EN

In 1872 G. Darboux defined a family of curves on surfaces of R³ 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).