The Weierstrass representation of discrete isotropic surfaces in R^2,1, R^3,1 and R^2,2

2009/07/03 by Dmitry Zakharov, Zakharov, Dmitry
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0907.0688

openalex publication_date 2009/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using an integrable discrete Dirac operator, we construct a discrete version of the Weierstrass representation of time-like surfaces parametrized along isotropic directions in R^2,1, R^3,1 and 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.

Citations

• A discrete analogue of the modified Novikov-Veselov hierarchy

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