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Mosc. Math. J., 2003, Volume 3, Number 2, Pages 419–438 (Mi mmj93)  

This article is cited in 26 scientific papers (total in 26 papers)

Geometry of the triangle equation on two-manifolds

I. A. Dynnikova, S. P. Novikovbc

a 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.


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MSC: 39A12 (39A70)
Received: September 5, 2002

Citation: I. A. Dynnikov, S. P. Novikov, “Geometry of the triangle equation on two-manifolds”, Mosc. Math. J., 3:2 (2003), 419–438

Citation in format AMSBIB
\by I.~A.~Dynnikov, S.~P.~Novikov
\paper Geometry of the triangle equation on two-manifolds
\jour Mosc. Math.~J.
\yr 2003
\vol 3
\issue 2
\pages 419--438

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