Beyond recursion operators

Yvette Kosmann-Schwarzbach

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arXiv · 1712.08908

Beyond recursion operators

Yvette Kosmann-Schwarzbach

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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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Yvette Kosmann-Schwarzbach. 2017-12-24. Beyond recursion operators. https://arxiv.org/abs/1712.08908

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