Integrability theorems of free systems and symplectic Haantjes structures

DOI10.7546/JGSP-63-2022-39-64OpenAlexW4226120814MaRDI QIDQ2110921

Keiichi Kikuchi, Tsukasa Takeuchi

Publication date: 23 December 2022

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

Full work available at URL: https://doi.org/10.7546/jgsp-63-2022-39-64

zbMATH Keywords

affine Killing vector fieldHaantjes operatorextended harmonic mapHamiltonian of free systemsymplectic-Haantjes manifold

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Differential geometric aspects of harmonic maps (53C43) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Lagrange's equations (70H03) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Cites Work

• Haantjes structures for the Jacobi-Calogero model and the Benenti systems
• Examples of four- or six-dimensional symplectic-Haantjes manifolds and about a relationship with recursion operators
• Beyond recursion operators
• EXTENDED HARMONIC MAPS AND LAGRANGE EQUATIONS
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