English

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.

Keywords

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

R2 v1 2026-06-24T04:18:27.384Z