The discrete centroaffine indefinite surface

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.