Title: 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.