Channel surfaces in Lie sphere geometry

Mason Pember; Gudrun Szewieczek

doi:10.1007/s13366-018-0394-6

Channel surfaces in Lie sphere geometry

Mason Pember
, Gudrun Szewieczek

Department of Mathematical Sciences

Technische Universität Wien

Research output: Contribution to journal › Article › peer-review

7 Citations (SciVal)

Abstract

We discuss channel surfaces in the context of Lie sphere geometry and characterise them as certain Ω ₀-surfaces. Since Ω 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.

Original language	English
Pages (from-to)	779-796
Number of pages	18
Journal	Beitraege zur Algebra und Geometrie
Volume	59
Issue number	4
Early online date	17 Apr 2018
DOIs	https://doi.org/10.1007/s13366-018-0394-6
Publication status	Published - 1 Nov 2018

Bibliographical note

Publisher Copyright:
© 2018, The Author(s).

Keywords

Channel surface
Integrable system
Legendre immersion
Lie sphere geometry
Polynomial conserved quantity
Ribaucour transformation

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.1007/s13366-018-0394-6Licence: CC BY

Cite this

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KW - Integrable system

KW - Legendre immersion

KW - Lie sphere geometry

KW - Polynomial conserved quantity

KW - Ribaucour transformation

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Channel surfaces in Lie sphere geometry

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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