On integrable systems outside Nijenhuis and Haantjes geometry

TL;DR

This paper explores non-invariant Killing tensors with non-zero Nijenhuis torsion in 3D Euclidean space, generalizing integrable systems to construct new superintegrable systems in higher dimensions.

Contribution

It introduces two new families of superintegrable systems in n-dimensional Euclidean space based on non-invariant Killing tensors with non-zero Nijenhuis torsion.

Findings

Construction of two new superintegrable systems families

Extension of integrable systems beyond Nijenhuis and Haantjes geometry

Analysis of non-invariant Killing tensors with non-zero Nijenhuis torsion

Abstract

We study non-invariant Killing tensors with non-zero Nijenhuis torsion in the three-dimensional Euclidean space. Generalizing the corresponding integrable systems we construct two new families of superintegrable systems in $n$-dimensional Euclidean space.