Mixed type of curves in the Lorentz-Minkowski space

For a non-lightlike non-degenerate regular curve, we have the arc-length parameter and the Frenet-Serret type formula by using a moving frame like as a regular space curve in the Euclidean space. If a point of the curve moves between spacelike and timelike regions, then there is a lightlike point. In this paper, we consider mixed types of not only regular curves but also curves with singular points. In order to consider mixed type of curves with singular points, we introduce a frame, so-called the lightcone frame, and lightcone framed curves. We investigate differential geometric properties of mixed type curves by using the lightcone frame.