Discrete constant mean curvature nets in space forms: Steiner's formula and Christoffel duality

TL;DR

This paper characterizes discrete principal nets in quadrics of constant curvature with constant mixed area mean curvature through the existence of a K"onigs dual in a concentric quadric, linking geometric properties with duality concepts.

Contribution

It introduces a novel characterization of discrete constant mean curvature nets in space forms using Christoffel duality and K"onigs duality in quadrics.

Findings

Discrete principal nets with constant mean curvature are characterized by K"onigs duality.

The work connects geometric curvature properties with duality in discrete differential geometry.

Provides a new framework for understanding discrete CMC nets in space forms.

Abstract

We show that the discrete principal nets in quadrics of constant curvature that have constant mixed area mean curvature can be characterized by the existence of a K\"onigs dual in a concentric quadric.