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arXiv · 2502.05646

Helix curves of the unit tangent bundle of a pseudo-Riemannian surface

Mohamed Tahar Kadaoui Abbassi·Khadija Boulagouaz
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Abstract

In this paper, we classify helix (spacelike, timelike and null) curves, directed by the geodesic flow vector field, on the (3-dimensional) unit tangent bundle of a pseudo-Riemannian surface of constant Gaussian curvature endowed with a pseudo-Riemannian $g$-natural metric of Kaluza-Klein type. We find, in particular, that every such helix curve is, in fact, a circular helix in the senses that its curvature and torsion are constant.

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Mohamed Tahar Kadaoui Abbassi, Khadija Boulagouaz. 2025-02-08. Helix curves of the unit tangent bundle of a pseudo-Riemannian surface. https://arxiv.org/abs/2502.05646

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