Multi-dimensional consistency of principal binets

Abstract

Principal binets are a discretization of curvature line parametrized surfaces defined on the vertices and faces of the square lattice ${\mathbb{Z}}^2$. They generalize the previously established discretizations given by circular nets, conical nets, and principal contact element nets. We show that principal binets constitute a discrete integrable system in the sense of multi-dimensional consistency. In particular, they generalize to higher-dimensional square lattices ${\mathbb{Z}}^N$. We also discuss relations to the notion of discrete orthogonal coordinate systems as previously established for discrete confocal quadrics.

28 pages, 10 figur