English

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 33-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}
}