This article is cited 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.

UDC: 514

Received: 14.09.2009

DOI: 10.4213/faa3029

 English version: Functional Analysis and Its Applications, 2011, 45:1, 25–32

Bibliographic databases:

• 
• 
• 
•