Channel linear Weingarten surfaces in space forms
arXiv:2105.00702 · doi:10.1007/s13366-022-00664-w
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.
27 pages, 8 figures, 5 tables