Examples of four- or six-dimensional symplectic-Haantjes manifolds and about a relationship with recursion operators (Q1980330)

It is well known that geodesic flows of the pseudo-Euclidean metrics in \(\mathbb R^n\) are the simplest examples of completely integrable systems. In this paper, by taking the Lorentz metric with \(n=2\) and \(n=3\), the associated Haantjes structure and recursion operators are constructed on four and six-dimensional linear symplectic spaces. The relation between recursion operators and Haantjes operators are investigated. For the entire collection see [Zbl 1468.53002].