Dupin cyclidic systems geometrically revisited
Differential Geometry
2022-01-24 v1
Abstract
The induced metrics of Dupin cyclidic systems, that is, orthogonal coordinate systems with Dupin cyclides and spheres as coordinate surfaces, were provided by Darboux. Here we take a more geometric point of view and discuss how Dupin cyclides and Lam\'e families of Dupin cyclidic systems can be obtained by suitably evolving an initial circle or a Dupin cyclide, respectively. This approach reveals that those Lam\'e families are given by parallel surfaces in various space forms.
Keywords
Cite
@article{arxiv.2201.08576,
title = {Dupin cyclidic systems geometrically revisited},
author = {Gudrun Szewieczek},
journal= {arXiv preprint arXiv:2201.08576},
year = {2022}
}
Comments
20 pages, 7 figures;