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arXiv · 1511.07579

A generalized Weierstrass representation of Lorentzian surfaces in $\mathbb{R}^{2,2}$ and applications

Victor Patty
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Abstract

We give a generalized Weierstrass formula for a Lorentz surface conformally immersed in the four-dimensional space $\mathbb{R}^{2,2}$ using spinors and Lorentz numbers. We also study the immersions of a Lorentzian surface in {\bf the} Anti-de Sitter space (a pseudo-sphere in $\mathbb{R}^{2,2}$): we give a new spinor representation formula and deduce the conformal description of a flat Lorentzian surface in that space.

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Victor Patty. 2016-02-29. A generalized Weierstrass representation of Lorentzian surfaces in $\mathbb{R}^{2,2}$ and applications. https://doi.org/10.1142/s0219887816500742

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