Björling problem for timelike surfaces in the Lorentz-Minkowski space

DOI10.1016/j.jmaa.2010.10.076zbMath1215.53014arXiv0906.2361OpenAlexW1996888974MaRDI QIDQ629203

Rosa Maria Barreiro Chaves, Martha P. Dussan, Martin A. Magid

Publication date: 8 March 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.2361

zbMATH Keywords

Björling problemLorentz-Minkowski spacetime-like surfaces

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (15)

Timelike surfaces in the de Sitter space \(\mathbb{S}_1^3(1)\subset \mathbb{R}_1^4\) ⋮ Timelike minimal surfaces in the three-dimensional Heisenberg group ⋮ Classification of zero mean curvature surfaces of separable type in Lorentz-Minkowski space ⋮ The Björling problem for timelike minimal surfaces in \({\mathbb {R}}^{4}_{1}\) ⋮ Minimal surfaces in Lorentzian Heisenberg group and Damek-Ricci spaces via the Weierstrass representation ⋮ Bonnet pairs of surfaces in Minkowski space ⋮ The Björling problem for timelike surfaces in \(\mathbb R_2^4\) ⋮ Weierstrass representations of Lorentzian minimal surfaces in \(\mathbb{R}^4_2\) ⋮ The Cauchy problem for indefinite improper affine spheres and their Hessian equation ⋮ The indefinite affine Cauchy problem ⋮ Enneper representation of minimal surfaces in the three-dimensional Lorentz-Minkowski space ⋮ A Weierstrass representation for minimal surfaces in 3-dimensional manifolds ⋮ Solutions of the Björling problem for timelike surfaces in the Lorentz-Minkowski space ⋮ The Björling problem for minimal surfaces in a Lorentzian three-dimensional Lie group ⋮ Explicit solving of the system of natural PDEs of minimal Lorentz surfaces in \(\mathbb{R}_2^4\)

Cites Work

• Classification of ruled surfaces in Minkowski 3-spaces
• Timelike minimal surfaces via loop groups
• Hyperbolic complex numbers and nonlinear sigma models
• Timelike surfaces in Lorentz 3-space with prescribed mean curvature and Gauss map
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• Ruled surfaces with pointwise 1-type Gauss map
• A geometric Cauchy problem for timelike minimal surfaces
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• On the Björling problem in a three-dimensional Lie group
• The affine Cauchy problem
• Björling problem for space-like, zero mean curvature surfaces in \(\mathbb L^{4}\)
• The Cauchy problem for improper affine spheres and the Hessian one equation
• Solutions of Minkowskian sigma models on hyperbolic complex Grassmann manifolds
• Björling problem for maximal surfaces in Lorentz–Minkowski space
• Geometrical interpretation of a generalized theory of gravitation
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