The normal map as a vector field
Differential Geometry
2022-09-12 v1
Abstract
In this paper we consider the normal map of a closed plane curve as a vector field on the cylinder. We interpret the critical points geometrically and study their Poincar\'{e} index, including the points at infinity. After projecting the vector field to the sphere we prove some counting theorems regarding the winding and rotation index of the curve and its evolute. We finish with a description of the extension to focal sets of surfaces.
Keywords
Cite
@article{arxiv.2209.04279,
title = {The normal map as a vector field},
author = {Thomas Waters and Matthew Cherrie},
journal= {arXiv preprint arXiv:2209.04279},
year = {2022}
}