On Laplace–Darboux-type sequences of generalized Weingarten surfaces

DOI10.1063/1.1286980zbMath0991.53003OpenAlexW2000116411MaRDI QIDQ2738205

Wolfgang K. Schief

Publication date: 30 August 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1286980

zbMATH Keywords

Painlevé equationBäcklund transformationLaplace transformationsgeneralized Weingarten surfacesBianchi surfacessurfaces of harmonic inverse mean curvature

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Surfaces in Euclidean and related spaces (53A05) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (5)

Weingarten hypersurfaces of the spherical type in Euclidean spaces ⋮ Generalized Weingarten surfaces of harmonic type in hyperbolic 3-space ⋮ Trapezoidal discrete surfaces: geometry and integrability ⋮ The Painlevé III, V and VI transcendents as solutions of the Einstein-Weyl equations ⋮ On the geometry of the Painlevé V equation and a Bäcklund transformation

Cites Work

• The reduction problem and the inverse scattering method
• From continuous to discrete Painlevé equations
• Surfaces with harmonic inverse mean curvature and Painlevé equations
• The Painlevé III, V and VI transcendents as solutions of the Einstein-Weyl equations
• Trapezoidal discrete surfaces: geometry and integrability
• Integrable Hamiltonian systems and interactions through quadratic constraints
• Description of the \(n\)-orthogonal curvilinear coordinate systems and Hamiltonian integrable systems of hydrodynamic type. I: Integration of the Lamé equations
• Generation of solutions of systems of partial differential equations by composition of infinitesimal Bäcklund transformations
• Nonlinear-Evolution Equations of Physical Significance
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• On a 2+1-dimensional Darboux system: integrable reductions
• On a 2+1-dimensional integrable Ernst-type equation
• On the geometry of an integrable (2+1)–dimensional sine–Gordon system
• Unified approach to strings and vortices with soliton solutions
• On generalized Loewner systems: Novel integrable equations in 2+1 dimensions
• SQUARED EIGENFUNCTIONS OF THE (MODIFIED) KP HIERARCHY AND SCATTERING PROBLEMS OF LOEWNER TYPE
• Binormal motion of curves of constant curvature and torsion. Generation of soliton surfaces
• On integrability of the inhomogeneous Heisenberg ferromagnet model: Examination of a new test

This page was built for publication: On Laplace–Darboux-type sequences of generalized Weingarten surfaces