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 Poincare 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.
|Journal||Balkan Journal of Geometry and Its Applications|
|Publication status||Accepted for publication - 15 Jan 2022|
- vector field
- normal map