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arXiv · 1508.04591

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

Zbigniew Olszak
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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 $τ=-2λs$, $s$ being the pseudo-arc parameter and $λ=\mathop{\rm constant}\not=0$.

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Zbigniew Olszak. 2015-08-19. A note about the torsion of null curves in the $3$-dimensional Minkowski spacetime and the Schwarzian derivative. https://doi.org/10.2298/fil1503553o

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