A note about the torsion of null curves in the $3$-dimensional Minkowski spacetime and the Schwarzian derivative

Abstract

The main topic of this paper is to show that in the 3-dimensional Minkowski spacetime, the torsion of a null curve is equal to the Schwarzian derivative of a certain function appearing in a description of the curve. As applications, we obtain descriptions of the slant helices, and null curves for which the torsion is of the form $\tau=-2\lambda s$, $s$ being the pseudo-arc parameter and $\lambda=\mathop{\rm constant}\not=0$.