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Geometry of the triangle equation on two-manifolds. (English) Zbl 1046.39016

A non-traditional approach to the discretization of differential-geometrical connections was suggested by the authors [Russ. Math. Surv. 52, No. 6, 1294–1295 (1997); translation from Usp. Mat. Nauk 52, No. 6, 157–158 (1997; Zbl 0928.39009)]. At the same time, they started with first-order difference “black-and-white triangle operators (equations)” on triangulated surfaces with a black-and-white coloring of triangles. In the present work, they develop a theory of these operators and equations showing their similarity to the complex derivatives \(\partial\) and \(-\partial\).
Reviewer: Fozi Dannan (Doha)

MathOverflow Questions:

Discrete-analytic functions

MSC:

39A70 Difference operators
39A12 Discrete version of topics in analysis

Citations:

Zbl 0928.39009
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