Surfaces in \(\mathbb{R}^ 3\) with prescribed curvature

DOI10.1016/0393-0440(94)00054-9zbMath0842.53004OpenAlexW2020506752MaRDI QIDQ1907143

Jacek Tafel

Publication date: 28 July 1996

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(94)00054-9

zbMATH Keywords

Ernst equation3-dimensional Minkowski spaceintegrability conditionsGauß curvatureGauß map

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Surfaces in Euclidean and related spaces (53A05) Exact solutions to problems in general relativity and gravitational theory (83C15) Local submanifolds (53B25) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (9)

A cohomological approach to immersed submanifolds via integrable systems ⋮ Properties of soliton surfaces associated with integrable $\mathbb{C}P^{N-1}$ sigma models ⋮ On geometric aspects of the supersymmetric Fokas–Gel’fand immersion formula ⋮ Geometric Formulation and Multi‐dark Soliton Solution to the Defocusing Complex Short Pulse Equation ⋮ A generalized formula for integrable classes of surfaces in Lie algebras ⋮ Deformations of surfaces associated with integrable Gauss–Mainardi–Codazzi equations ⋮ The multicomponent Ernst equation and the Moutard transformation ⋮ Bäcklund transformations for hyperbolic surfaces in \(E^3\) via Weingarten congruences ⋮ On a discretization of asymptotic nets

Cites Work

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• On some integrable cases in surface theory
• Bianchi surfaces in \(\mathbb{R}^ 3\) and deformation of hyperelliptic curves
• Integrable Hamiltonian systems and interactions through quadratic constraints
• Two-dimensional reductions of the self-dual Yang–Mills equations in self-dual spaces
• The Large Scale Structure of Space-Time

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