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

Details The Weierstrass representation of discrete isotropic surfaces in $R^{2,1}$, $R^{3,1}$ and $R^{2,2}$ The Weierstrass representation of discrete isotropic surfaces in $R^{2,1}$, $R^{3,1}$ and $R^{2,2}$

2009-07-03

arxiv.org/abs/0907.0688v1

Mathematics

Differential Geometry

Scientific paper

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.

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