Geometric deformations of curves in the Minkowski plane

TL;DR

This paper extends a geometric deformation method to curves in the Minkowski plane, analyzing local phenomena, singularities, and evolutes during deformations, providing detailed insights into their geometric behavior.

Contribution

It introduces a comprehensive approach to study curve deformations in the Minkowski plane, including singularities and evolutes, expanding prior methods to this geometric setting.

Findings

Detailed analysis of inflections, vertices, and lightlike points during deformations

Behavior of evolutes and caustics at special points

Classification of bifurcations in curve deformations

Abstract

In this paper, we extend the method developed in [17, 18] to curves in the Minkowski plane. The method proposes a way to study deformations of plane curves taking into consideration their geometry as well as their singularities. We deal in detail with all local phenomena that occur generically in 2-parameters families of curves. In each case, we obtain the geometry of the deformed curve, that is, information about inflections, vertices and lightlike points. We also obtain the behavior of the evolute/caustic of a curve at especial points and the bifurcations that can occur when the curve is deformed.