Geometric deformations of curves in the Minkowski plane

Abstract

In this paper, we propose a method to study plane curves deformations in the Minkowski plane taking into consideration their geometry as well as their singularities. This method is an extension of the method proposed by Salarinoghabi and Tari to curves in the Euclidean plane. 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.