Poisson brackets associated to the conformal geometry of curves

DOI10.1090/S0002-9947-04-03589-5zbMath1081.37042OpenAlexW1573986664MaRDI QIDQ4663486

Gloria Marí Beffa

Publication date: 31 March 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-04-03589-5

zbMATH Keywords

Hamiltonian structurecompletely integrable systemsconformal differential invariantsHasimoto transformationreduced Poisson bracketinvariant flowcurves in the Möbius sphere

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) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Differential invariants (local theory), geometric objects (53A55)

Related Items (10)

Integrable motions of curves in \(S^{1} \times \mathbb R\) ⋮ Geometry of curves in generalized flag varieties ⋮ A nonlocal Poisson bracket of the sine-Gordon model ⋮ Poisson structures for geometric curve flows in semi-simple homogeneous spaces ⋮ On geometry of curves of flags of constant type ⋮ Projective-type differential invariants and geometric curve evolutions of KdV-type in flat homogeneous manifolds ⋮ Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces ⋮ Construction of Rational Curves with Rational Rotation-Minimizing Frames via Möbius Transformations ⋮ Hamiltonian evolution of curves in classical affine geometries ⋮ Integrable systems inn-dimensional conformal geometry

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