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

Zbigniew Olszak


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 $\lambda=\const\neq0$.

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