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.