Moving frames, geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors

DOI10.5802/aif.2678zbMath1245.53066OpenAlexW2264340996MaRDI QIDQ424844

Gloria Marí Beffa

Publication date: 6 June 2012

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/219747

zbMATH Keywords

Miura transformationmoving framedifferential invariantsgeometric Poisson bracketsKdV equationsnon-commutative modified KdV systemspinor evolutions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Deformation quantization, star products (53D55)

Related Items (2)

On geometry of curves of flags of constant type ⋮ Dirac-Lie systems and Schwarzian equations

Cites Work

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• The moving frame, differential invariants and rigidity theorems for curves in homogeneous spaces
• Bi-Hamiltonian flows and their realizations as curves in real semisimple homogeneous manifolds
• Poisson structures for geometric curve flows in semi-simple homogeneous spaces
• Group actions on chains of Banach manifolds and applications to fluid dynamics
• Projective-type differential invariants and geometric curve evolutions of KdV-type in flat homogeneous manifolds
• Geometric realizations of bi-Hamiltonian completely integrable systems
• Geometric Hamiltonian structures on flat semisimple homogeneous manifolds
• Remarks on KdV-type flows on star-shaped curves
• On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry
• Lagrange-Schwarzian derivative and symplectic Sturm theory
• Moving coframes. II: Regularization and theoretical foundations
• Poisson geometry of the filament equation
• Moving coframes. I: A practical algorithm
• Integrable equations arising from motions of plane curves. II.
• Geometric realizations of Fordy-Kulish nonlinear Schrödinger systems.
• Integrable systems in three-dimensional Riemannian geometry.
• Hamiltonian flows of curves in \(G/\text{SO}(N)\) and vector soliton equations of mKdV and sine-Gordon type
• Evolution of curvature invariants and lifting integrability
• Geometric Poisson brackets on Grassmannians and conformal spheres
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• Complex Paraconformal Manifolds – their Differential Geometry and Twistor Theory
• Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations
• Integrable systems associated to curves in flat Galilean and Minkowski spaces
• The geometry of the KdV equation
• A new flow on starlike curves in $\mathbb {R}^3$
• Conformal Circles and Parametrizations of Curves in Conformal Manifolds
• A soliton on a vortex filament
• On completely integrable geometric evolutions of curves of Lagrangian planes
• The Conformal Theory of Curves
• Completely integrable curve flows on adjoint orbits
• Integrable equations arising from motions of plane curves

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