Timelike minimal surfaces in the three-dimensional Heisenberg group

DOI10.1007/s12220-022-00962-8zbMath1500.53075arXiv2203.03834OpenAlexW4226465294WikidataQ114221007 ScholiaQ114221007MaRDI QIDQ2149960

Shimpei Kobayashi, Hirotaka Kiyohara

Publication date: 27 June 2022

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.03834

zbMATH Keywords

Heisenberg groupminimal surfacesloop groupsgeneralized Weierstrass type representationtime-like surfacesnon-linear Dirac equation

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Harmonic maps, etc. (58E20)

Cites Work

• A loop group method for minimal surfaces in the three-dimensional Heisenberg group
• The geometric Cauchy problem for surfaces with Lorentzian harmonic Gauss maps
• Timelike constant mean curvature surfaces with singularities
• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• Björling problem for timelike surfaces in the Lorentz-Minkowski space
• Enneper representation of minimal surfaces in the three-dimensional Lorentz-Minkowski space
• Timelike minimal surfaces via loop groups
• Immersions of Lorentzian surfaces in \(\mathbb R^{2,1}\)
• Timelike surfaces in Lorentz 3-space with prescribed mean curvature and Gauss map
• Lorentz metrics on unimodular Lie groups of dimension three
• Timelike surfaces of constant mean curvature in Minkowski 3-space
• Weierstrass type representation of harmonic maps into symmetric spaces
• Application of soliton theory to the construction of pseudospherical surfaces in \(\mathbb{R}^ 3\)
• A Weierstrass representation for minimal surfaces in 3-dimensional manifolds
• An introduction to Lorentz surfaces
• Minimal surfaces in Lorentzian Heisenberg group and Damek-Ricci spaces via the Weierstrass representation
• Generalized Weierstrass-Enneper representations of Euclidean, spacelike, and timelike surfaces: a unified Lie-algebraic formulation
• Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space
• A Weierstrass representation theorem for Lorentz surfaces
• The Björling problem for minimal surfaces in a Lorentzian three-dimensional Lie group
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Timelike minimal surfaces in the three-dimensional Heisenberg group