A generalized Weierstrass representation of Lorentzian surfaces in ℝ2,2 and applications

DOI10.1142/S0219887816500742zbMath1342.53017arXiv1511.07579OpenAlexW3105502784MaRDI QIDQ5739630

Victor Patty

Publication date: 19 July 2016

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.07579

zbMATH Keywords

immersionsspinorsWeierstrass representationLorentz surfaces

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Spin and Spin({}^c) geometry (53C27) Local submanifolds (53B25) Non-Euclidean differential geometry (53A35) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (5)

Spinorial representation of submanifolds in \(\mathrm{SL}_n(\mathbb{C})/\mathrm{SU}(n)\) ⋮ Weierstrass representations of Lorentzian minimal surfaces in \(\mathbb{R}^4_2\) ⋮ Spinorial representation of submanifolds in metric Lie groups ⋮ Explicit solving of the system of natural PDEs of minimal Lorentz surfaces in \(\mathbb{R}_2^4\) ⋮ Spinorial representation of surfaces in Lorentzian homogeneous spaces of dimension 3

Cites Work

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• The Björling problem for timelike surfaces in \(\mathbb R_2^4\)
• Weierstrass representation for timelike minimal surfaces in Minkowski 3-space
• An introduction to Lorentz surfaces
• Weierstrass representations for surfaces in 4D spaces and their integrable deformations via DS hierarchy
• A Weierstrass representation theorem for Lorentz surfaces

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