Cyclic surfaces in \(\mathbb{E}^5\) generated by equiform motions
Cyclides were detected and first studied by C. Dupin (Dupin cyclides). They are defined as the envelope of two families of general quadrics such that each of these quadrics is tangent to the surface along the conics, with the additional property that the two families of contact conics establish a conjugate net on the surface (supercyclides). Other generalisations result in so-called cyclic surfaces. These surfaces can be generated by equiform motions of a circle. In this paper the authors study cyclic surfaces in \(\mathbb{E}^5\) generated by equiform motions of a circle. Properties of these cyclic surfaces up to the first-order are discussed. The authors prove the following new result: A cyclic 2-surface in \(\mathbb{E}^5\) in general is contained in a canal hypersurface. Finally, they give an example.
scientific article; zbMATH DE number 2101770