Examples of Four- or Six-Dimensional Symplectic-Haantjes Manifolds and About a Relationship with Recursion Operators

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.