• Corpus ID: 204960800

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

  title={The equi-affine curvatures of curves in 3-dimensional pseudo-Riemannian manifolds.},
  author={Karina Olszak and Zbigniew Olszak},
  journal={arXiv: Differential Geometry},
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… 



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  • Declan Davis
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2006
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