The Relationship Between the Frenet Frame and the Lightcone Frame of a Mixed-Type Curve in Minkowski 3-Space

Abstract

In the present paper, we give the relationship between the Frenet frame and the lightcone frame of a mixed-type curve. We present the curvature kappa and the torsion tau of a mixed-type curve in terms of its lightcone semi-polar coordinates. Finally, the Darboux vector of the curve is expressed as a linear combination of the lightcone frame and the lightcone semi-polar coordinates.