Dupin cyclidic systems geometrically revisited

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 Lamé families of Dupin cyclidic systems can be obtained by suitably evolving an initial circle or a Dupin cyclide, respectively. This approach reveals that those Lamé families are given by parallel surfaces in various space forms.

20 pages, 7 figures;