Evolutes of the (n,m)-cusp mixed-type curves in the Lorentz–Minkowski plane

Abstract

The evolute of a regular curve in the Lorentz–Minkowski plane is given by the locus of centers of osculating pseudo-circle of the base curve. But the case when a curve has singularities is not very clear. In this paper, we use lightcone frame to define the [Formula: see text]-cusp mixed-type curves and their evolutes in Lorentz–Minkowski plane. In order to attain this goal, we define the [Formula: see text]-cusp non-lightlike curves and their evolutes in Lorentz–Minkowski plane first. Then we study the behaviors of the evolutes of the [Formula: see text]-cusp mixed-type curves at the [Formula: see text]-cusp.