This article is cited in 37 papers

Geometry of the triangle equation on two-manifolds

I. A. Dynnikov^a, S. P. Novikov<sup>bc

a</sup> M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
^c University of Maryland

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 the present work, we develop a theory of these operators and equations showing their similarity to the complex derivatives $\partial$ and $\bar\partial$.

Key words and phrases: Discrete connection, discrete analog of complex derivatives, triangle equation, first order difference operator.

MSC: 39A12 (39A70)

Received: September 5, 2002

Language: English

DOI: 10.17323/1609-4514-2003-3-2-419-438

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