Classification of 34 Haantjes structures on h4 Lie algebra yields three new integrable sigma models on H4 via deformation of the chiral model under solved integrability conditions.
Beyond recursion operators
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abstract
We briefly recall the history of the Nijenhuis torsion of (1,1)-tensors on manifolds and of the lesser-known Haantjes torsion. We then show how the Haantjes manifolds of Magri and the symplectic-Haantjes structures of Tempesta and Tondo generalize the classical approach to integrable systems in the bi-hamiltonian and symplectic-Nijenhuis formalisms, the sequence of powers of the recursion operator being replaced by a family of commuting Haantjes operators.
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Integrable sigma models with Haantjes structure on ${H_{4}}$ Lie group
Classification of 34 Haantjes structures on h4 Lie algebra yields three new integrable sigma models on H4 via deformation of the chiral model under solved integrability conditions.