Weierstrass representation for discrete isotropic surfaces in ℝ2,1, ℝ3,1, and ℝ2,2

Abstract

Using an integrable discrete Dirac operator, we construct a discrete version of the Weierstrass representation for hyperbolic surfaces parameterized along isotropic directions in ℝ2,1, ℝ3,1, and ℝ2,2. 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.