Mixed type curves in Minkowski 3-space (Singularity theory of differentiable maps and their applications)

Abstract

In this paper, we study mixed type curves in Minkowski 3-space. Mixed type curves are regular curves, and there are both non-lightlike points and lightlike points in a mixed type curve. For non-lightlike curves and null curves in Minkowski 3-space, we can study them by a Frenet frame or a Cartan frame respectively. But for mixed type curves, the two frames will not work. And as far as we know, no one has yet given a frame to study them in Minkowski 3-space. So we give the lightcone frame in order to provide a tool for studying this type curves in mathematical and physical research. As an application of the lightcone frame, we define an evolute of a mixed type curve. And we also give some examples to show the evolutes.