Channel linear Weingarten surfaces in space forms

Udo Hertrich-Jeromin, Mason Pember, Denis Polly

Research output: Contribution to journalArticlepeer-review

Abstract

Channel linear Weingarten surfaces in space forms are investigated in a Lie sphere geometric setting, which allows for a uniform treatment of different ambient geometries. We show that any channel linear Weingarten surface in a space form is isothermic and, in particular, a surface of revolution in its ambient space form. We obtain explicit parametrisations for channel surfaces of constant Gauss curvature in space forms, and thereby for a large class of linear Weingarten surfaces up to parallel transformation.

Original languageEnglish
JournalBeitrage zur Algebra und Geometrie
Early online date23 Jan 2023
DOIs
Publication statusE-pub ahead of print - 23 Jan 2023

Keywords

  • Channel surface
  • Constant Gauss curvature
  • Isothermic sphere congruence
  • Isothermic surface
  • Jacobi elliptic function
  • Lie sphere geometry
  • Linear Weingarten surface
  • Omega surface

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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