Dynamical behavior of Darboux curves
Differential Geometry
2009-12-21 v1 Dynamical Systems
Abstract
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).
Cite
@article{arxiv.0912.3749,
title = {Dynamical behavior of Darboux curves},
author = {Ronaldo Garcia and Remi Langevin and Pawel Walczak},
journal= {arXiv preprint arXiv:0912.3749},
year = {2009}
}
Comments
44 pages, 17 figures