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arXiv · 1910.13783

The equi-affine curvatures of curves in 3-dimensional pseudo-Riemannian manifolds

Karina Olszak·Zbigniew Olszak
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Abstract

In this paper, the Cartan frames and the equi-affine curvatures are described with the help of the Frenet frames and the Frenet curvatures of a non-null and non-degenerate curve in a 3-dimensional pseudo-Riemannian manifold. The constancy of the Frenet curvatures of such a curve always implies the constancy of the equi-affine curvatures. We show that the converse statement does not hold in general. Finally, we study the equi-affine curvatures of null curves in 3-dimensional Lorentzian manifolds, and prove that they are related to their pseudo-torsion.

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Karina Olszak, Zbigniew Olszak. 2019-10-30. The equi-affine curvatures of curves in 3-dimensional pseudo-Riemannian manifolds. https://arxiv.org/abs/1910.13783

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