Geometry of the triangle equation on two–manifolds

Abstract

A non-traditional approach to the discretization of differential-geometrical connections was suggested by the authors in 1997. At the same time we started studying first order difference “black and white triangle operators (equations) ” on triangulated surfaces with a black and white coloring of triangles. In this work, we develop the theory of these operators and equations, showing their similarity with the complex derivatives ∂ and ∂.