Channel linear Weingarten surfaces

TL;DR

This paper classifies non-tubular channel linear Weingarten surfaces in Euclidean space, showing they are surfaces of revolution related to catenoids or surfaces with constant Gauss curvature, and provides explicit parametrizations.

Contribution

It proves that all non-tubular channel linear Weingarten surfaces are surfaces of revolution and offers explicit parametrizations and existence results for complete hyperbolic cases.

Findings

Non-tubular channel linear Weingarten surfaces are surfaces of revolution.

Explicit parametrizations of these surfaces are provided.

Existence of complete hyperbolic linear Weingarten surfaces is established.

Abstract

We demonstrate that every non-tubular channel linear Weingarten surface in Euclidean space is a surface of revolution, hence parallel to a catenoid or a rotational surface of non-zero constant Gauss curvature. We provide explicit parametrizations and deduce existence of complete hyperbolic linear Weingarten surfaces.