English

Conformal invariants of curves via those for inscribed polygons with circular edges

Differential Geometry 2024-02-01 v1 High Energy Physics - Theory Mathematical Physics math.MP

Abstract

The conformal nature of smooth curves in R3\mathbb{R}^3 is characterised by conformal length, curvature and torsion. We present a derivation of these conformal parameters via a limiting process using inscribed polygons with circular edges . The procedure is based on elementary geometry in R3\mathbb{R}^3 only and similar to the rectification of curves in the metrical case. It seems to be not available in the literature so far.

Keywords

Cite

@article{arxiv.2401.17854,
  title  = {Conformal invariants of curves via those for inscribed polygons with circular edges},
  author = {Harald Dorn},
  journal= {arXiv preprint arXiv:2401.17854},
  year   = {2024}
}

Comments

9 pages, 2 figures