Channel linear Weingarten surfaces in space forms

被引：1

作者：

Hertrich-Jeromin, Udo ^{[1
]}

Pember, Mason ^{[2
]}

Polly, Denis ^{[3
]}

机构：

[1] TU Wien, Inst Discrete Math & Geometry, Wiedner Hauptstr 8-10-104, A-1040 Vienna, Austria

[2] Univ Bath, Dept Math Sci, Bath BA2 7AY, England

[3] Kobe Univ, Dept Math, 1-1 Rokkodai Cho,Nada Ku, Kobe 6578501, Japan

来源：

BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY | 2023年 / 64卷 / 04期

关键词：

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

D O I：

10.1007/s13366-022-00664-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：969 / 1009

页数：41

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