Curvature types of planar curves for gauges
Differential Geometry
2019-10-02 v1
Abstract
In this paper results from the differential geometry of curves are extended from normed planes to gauge planes which are obtained by neglecting the symmetry axiom. Based on the gauge analogue of the notion of Birkhoff orthogonality from Banach space theory, we study all curvature types of curves in gauge planes, thus generalizing their complete classification for normed planes. We show that (as in the subcase of normed planes) there are four such types, and we call them analogously Minkowski, normal, circular, and arc-length curvature. We study relations between them and extend, based on this, also the notions of evolutes and involutes to gauge planes.
Keywords
Cite
@article{arxiv.1910.00281,
title = {Curvature types of planar curves for gauges},
author = {Vitor Balestro and Horst Martini and Makoto Sakaki},
journal= {arXiv preprint arXiv:1910.00281},
year = {2019}
}