Year: 2022
Type: preprint
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 Poincaré 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.
Source: arXiv (Cornell University)
Authors: Waters, Thomas, Cherrie, Matthew
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4297793605