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

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.

arXiv admin note: text overlap with arXiv:1410.7313. To appear in the International Journal of Geometric Methods in Modern Physics

References in corpus (1)

• Spinor representation of Lorentzian surfaces in R^{2,2}

Cited by in corpus (3)

• Spinorial representation of submanifolds in metric Lie groups
• Weierstrass Representations of Lorentzian Minimal Surfaces in ${\mathbb{R}}_2^4$
• Spinorial representation of surfaces in Lorentzian homogeneous spaces of dimension 3