2022/01/21 by Gudrun Szewieczek, Szewieczek, Gudrun
Engineering · #53A05 #53A35 #53C12 (primary) #53E99 (secondary) #Control and Dynamics of Mobile Robots #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2201.08576
openalex publication_date 2022/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.