Abstract.
We study the class of plane curves with positive curvature κ and spherical parametrization s. t. that the curves and their derived curves like evolute, caustic, pedal and co-pedal curve, resp., have the same shape. We characterize these properties by a homogeneous linear differential equation of first order for the support function ρ and the radii of curvature κ -1 and we give a complete local classification of this class.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Udo Simon on the occasion of his 70th birthday
Received: February 15, 2008. Revised: June 5, 2008. Accepted: June 5, 2008.
Rights and permissions
About this article
Cite this article
Schwenk-Schellschmidt, A. Pedal Curves Part I: Homogeneous Differential Equation. Result. Math. 52, 369–382 (2008). https://doi.org/10.1007/s00025-008-0319-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-008-0319-z