Beyond recursion operators
History and Overview
2017-12-27 v1 Differential Geometry
Dynamical Systems
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.
Cite
@article{arxiv.1712.08908,
title = {Beyond recursion operators},
author = {Yvette Kosmann-Schwarzbach},
journal= {arXiv preprint arXiv:1712.08908},
year = {2017}
}
Comments
Talk at the XXXVI Workshop on Geometric Methods in Physics, Poland, July 2017. To appear in the proceedings