Lie sphere geometry and integrable systems.

DOI10.2748/tmj/1178224607zbMath1058.53012OpenAlexW1980781102MaRDI QIDQ1587377

Evgeny V. Ferapontov

Publication date: 2000

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178224607

zbMATH Keywords

Willmore functionalcyclidic surfacesLie-minimal surfaceTzitzeica system

Mathematics Subject Classification ID

Related Items (8)

ANALOG OF WILCZYNSKI'S PROJECTIVE FRAME IN LIE SPHERE GEOMETRY: LIE-APPLICABLE SURFACES AND COMMUTING SCHRÖDINGER OPERATORS WITH MAGNETIC FIELDS ⋮ Lie applicable surfaces and curved flats ⋮ Deformation and applicability of surfaces in Lie sphere geometry ⋮ \(G\)-deformations of maps into projective space ⋮ Constrained elastic curves and surfaces with spherical curvature lines ⋮ Projective differential geometry of higher reductions of the two-dimensional Dirac equation ⋮ Fast, robust, and faithful methods for detecting crest lines on meshes ⋮ On the Cauchy problem for the integrable system of Lie minimal surfaces

Cites Work

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• Veselov-Novikov equation as a natural two-dimensional generalization of the Korteweg-de Vries equation
• Bäcklund transformations and their applications
• Nonlinear oscillations of hyperbolic systems: Methods and qualitative results
• Dupin hypersurfaces and a Lie invariant
• Surfaces of Demoulin: Differential geometry, Bäcklund transformation and integrability
• Surfaces of revolution in terms of solitons
• On integrability of \(3 \times{}3\) semi-Hamiltonian hydrodynamic type systems \(u_ t^ i = v_ j^ i (u) u_ x^ j\) which do not possess Riemann invariants
• Stationary Veselov-Novikov equation and isothermally asymptotic surfaces in projective differential geometry
• Dupin hypersurfaces and integrable Hamiltonian systems of hydrodynamic type which do not possess Riemann invariants
• On the geometry of an integrable (2+1)–dimensional sine–Gordon system
• Modified Novikov--Veselov equation and differential geometry of surfaces
• THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
• Induced Surfaces and Their Integrable Dynamics
• Lie sphere geometry. With applications to submanifolds
• Surfaces with flat normal bundle: An explicit construction
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