Channel surfaces in Lie sphere geometry
classification
🧮 math.DG
keywords
surfaceschannelcertaincharacterisegeometryomegaspherebehaviour
read the original 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.
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