Examples of Four- Or Six-Dimensional Symplectic-Haantjes Manifolds and About A Relationship with Recursion Operators

Takeuchi, Tsukasa

doi:10.7546/giq-22-2021-263-273

VOL. 22 | 2021 Examples of Four- Or Six-Dimensional Symplectic-Haantjes Manifolds and About A Relationship with Recursion Operators

Tsukasa Takeuchi

Editor(s) Ivaïlo M. Mladenov, Vladimir Pulov, Akira Yoshioka

Geom. Integrability & Quantization, 2021: 263-273 (2021) DOI: 10.7546/giq-22-2021-263-273

Abstract

Certain ways of characterizing integrable systems with (1, 1)-tensor field have been investigated, so far. For example, recursion operators and Haantjes operators are known. We show that geometrical examples of four- or six-dimensional symplectic Haantjes manifolds and recursion operators for several Hamiltonian systems. Through these examples, we consider the relation between recursion operators and Haantjes operators.