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 or triangles. In this work, we develop the theory of these operators and equations, showing their similarity with complex derivatives.

latex, 23 pages, 10 figures

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