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Zbl 1046.39016
Dynnikov, I. A.; Novikov, S. P.
Geometry of the triangle equation on two-manifolds.
(English)
[J] Mosc. Math. J. 3, No. 2, 419-438 (2003). ISSN 1609-3321

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 $-\partial$.
[Fozi Dannan (Doha)]
MSC 2000:
*39A70 Difference operators
39A12 Discrete version of topics in analysis

Keywords: discrete connection; discrete analog of complex derivatives; triangle equation; first-order difference operator

Citations: Zbl 0928.39009

Cited in: Zbl 1141.39019

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