Channel surfaces in Lie sphere geometry

Abstract

We discuss channel surfaces in the context of Lie sphere geometry and characterise them as certain ${\Omega }_0$-surfaces. Since ${\Omega }_0$-surfaces possess a rich transformation theory, we study the behaviour of channel surfaces under these transformations. Furthermore, by using certain Dupin cyclide congruences, we characterise Ribaucour pairs of channel surfaces.

14 pages, 2 figures

References in corpus (4)

• Semi-discrete isothermic surfaces
• Lie applicable surfaces
• Polynomial Conserved Quantities of Lie Applicable Surfaces
• Ribaucour coordinates

Cited by in corpus (4)

• Discrete channel surfaces
• Ribaucour coordinates
• Channel linear Weingarten surfaces in space forms
• Behavior of principal curvatures of frontals near non-front singular points and their application