The discrete centroaffine indefinite surface

TL;DR

This paper develops the mathematical framework for discrete centroaffine indefinite surfaces in three-dimensional space, including structure equations, invariants, and properties like Laplacian and convexity, with illustrative examples.

Contribution

It introduces the structure equations and invariants for discrete centroaffine indefinite surfaces, advancing the understanding of their geometric and integrable properties.

Findings

Derived structure equations and invariants for the surfaces

Analyzed Laplacian operator and convexity properties

Provided illustrative examples of the surfaces

Abstract

In this paper we build the structure equations and the integrable systems for a discrete centroaffine indefinite surface in $\R^3$. At the same time, some centroaffine invariants are obtained according to the structure equations. Using these centroaffine invariants, we study the Laplacian operator and the convexity of a discrete centroaffine indefinite surface. Furthermore, some interest examples are provided.