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

2024/01/31 by Dorn, Harald
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2401.17854

Abstract

The conformal nature of smooth curves in ℝ3 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 only and similar to the rectification of curves in the metrical case. It seems to be not available in the literature so far.

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