Evolutes Of The(N,M)-Cusp Mixed-Type Curves In The Lorentz-Minkowski Plane

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 (n,m)-cusp mixed-type curves and their evolutes in Lorentz-Minkowski plane. In order to attain this goal, we define the (n,m)-cusp non-lightlike curves and their evolutes in Lorentz-Minkowski plane first. Then we study the behaviors of the evolutes of the (n,m)-cusp mixed-type curves at the (n,m)-cusp.