Evolutes of plane curves and null curves in Minkowski $3$-space
Differential Geometry
2016-05-10 v1
Abstract
We use the isotropic projection of Laguerre geometry in order to establish a correspondence between plane curves and null curves in the Minkowski -space. We describe the geometry of null curves (Cartan frame, pseudo-arc parameter, pseudo-torsion, pairs of associated curves) in terms of the curvature of the corresponding plane curves. This leads to an alternative description of all plane curves which are Laguerre congruent to a given one.
Keywords
Cite
@article{arxiv.1605.02117,
title = {Evolutes of plane curves and null curves in Minkowski $3$-space},
author = {Boaventura Nolasco and Rui Pacheco},
journal= {arXiv preprint arXiv:1605.02117},
year = {2016}
}