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arXiv · 1709.02224

Channel surfaces in Lie sphere geometry

Mason Pember·Gudrun Szewieczek
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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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Mason Pember, Gudrun Szewieczek. 2017-09-07. Channel surfaces in Lie sphere geometry. https://doi.org/10.1007/s13366-018-0394-6

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