DISCRETE LINEAR WEINGARTEN SURFACES

Abstract

Discrete linear Weingarten surfaces in space forms are characterized as special discrete $\unicode[STIX]{x1D6FA}$ -nets, a discrete analogue of Demoulin’s $\unicode[STIX]{x1D6FA}$ -surfaces. It is shown that the Lie-geometric deformation of $\unicode[STIX]{x1D6FA}$ -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.