The Singular Evolutoids Set and the Extended Evolutoids Front
Differential Geometry
2022-03-09 v2
Abstract
In this paper we introduce the notion of the singular evolutoid set which is the set of all singular points of all evolutoids of a fixed smooth planar curve with at most cusp singularities. By the Gauss-Bonnet Theorem for Coherent Tangent Bundles over Surfaces with Boundary (Theorem 2.20 in [4]) applied to the extended front of evolutoids of a hedgehog we obtain an integral equality for smooth periodic curves.
Cite
@article{arxiv.2107.08605,
title = {The Singular Evolutoids Set and the Extended Evolutoids Front},
author = {M. Zwierzyński},
journal= {arXiv preprint arXiv:2107.08605},
year = {2022}
}
Comments
15 pages, 9 figures