Discrete linear Weingarten surfaces

TL;DR

This paper introduces a discrete analogue of linear Weingarten surfaces in space forms, characterizing them as special discrete Omega-nets and exploring their Lie-geometric deformations and Lawson transformations.

Contribution

It establishes a novel discrete framework for linear Weingarten surfaces and links Lie-geometric deformations to Lawson transformations, extending classical concepts.

Findings

Discrete linear Weingarten surfaces characterized as special Omega-nets

Lie-geometric deformation induces Lawson transformation

Lawson correspondence recovered in the constant mean curvature case

Abstract

Discrete linear Weingarten surfaces in space forms are characterized as special discrete $\Omega$-nets, a discrete analogue of Demoulin's $\Omega$-surfaces. It is shown that the Lie-geometric deformation of $\Omega$-nets descends to a Lawson transformation for discrete linear Weingarten surfaces, which coincides with the well-known Lawson correspondence in the constant mean curvature case.