The Geometry of the Secant Caustic of a Planar Curve
Differential Geometry
2021-06-08 v3
Abstract
The secant caustic of a planar curve is the image of the singular set of the secant map of . We analyse the geometrical properties of the secant caustic of a planar curve, i.e. the number of branches of the secant caustic, the parity of the number of cusps and the number of inflexion points in each branch of this set. In particular, we investigate in detail some of the geometrical properties of the secant caustic of a rosette, i.e. a smooth regular oriented closed curve with non-vanishing curvature.
Cite
@article{arxiv.1803.00084,
title = {The Geometry of the Secant Caustic of a Planar Curve},
author = {W. Domitrz and M. C. Romero Fuster and M. Zwierzyński},
journal= {arXiv preprint arXiv:1803.00084},
year = {2021}
}
Comments
23 pages, 11 figures