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Funktsional. Anal. i Prilozhen., 2011, Volume 45, Issue 1, Pages 31–40 (Mi faa3029)  

This article is cited in 1 scientific paper (total in 1 paper)

Weierstrass Representation for Discrete Isotropic Surfaces in $\mathbb{R}^{2,1}$, $\mathbb{R}^{3,1}$, and $\mathbb{R}^{2,2}$

D. V. Zakharov

Columbia University

Abstract: Using an integrable discrete Dirac operator, we construct a discrete version of the Weierstrass representation for hyperbolic surfaces parameterized along isotropic directions in $\mathbb{R}^{2,1}$, $\mathbb{R}^{3,1}$, and $\mathbb{R}^{2,2}$. The corresponding discrete surfaces have isotropic edges. We show that any discrete surface satisfying a general monotonicity condition and having isotropic edges admits such a representation.

Keywords: integrable system, discretization, discrete differential geometry

DOI: https://doi.org/10.4213/faa3029

Full text: PDF file (184 kB)
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English version:
Functional Analysis and Its Applications, 2011, 45:1, 25–32

Bibliographic databases:

UDC: 514
Received: 14.09.2009

Citation: D. V. Zakharov, “Weierstrass Representation for Discrete Isotropic Surfaces in $\mathbb{R}^{2,1}$, $\mathbb{R}^{3,1}$, and $\mathbb{R}^{2,2}$”, Funktsional. Anal. i Prilozhen., 45:1 (2011), 31–40; Funct. Anal. Appl., 45:1 (2011), 25–32

Citation in format AMSBIB
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\paper Weierstrass Representation for Discrete Isotropic Surfaces in $\mathbb{R}^{2,1}$, $\mathbb{R}^{3,1}$, and~$\mathbb{R}^{2,2}$
\jour Funktsional. Anal. i Prilozhen.
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\vol 45
\issue 1
\pages 31--40
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Tsuchida T., Dimakis A., “On a (2+1)-dimensional generalization of the Ablowitz-Ladik lattice and a discrete Davey-Stewartson system”, J. Phys. A, 44:32 (2011), 325206, 20 pp.  crossref  mathscinet  zmath  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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