On Haantjes tensors for second-order superintegrable systems

TL;DR

This paper explores the role of Haantjes tensors in second-order superintegrable systems, linking tensor vanishing to integrability and separation coordinates, with a focus on conservation laws and Killing tensors.

Contribution

It introduces the study of Haantjes-zero Killing tensors in superintegrable systems, highlighting their significance for integrability and coordinate separation.

Findings

Haantjes tensor vanishing relates to integrability

Killing tensors with zero Haantjes tensor are key in superintegrable systems

Provides new insights into the geometric structure of superintegrable systems

Abstract

The vanishing of the Haantjes tensor is an important property that has been linked, for instance, to the existence of separation coordinates and the integrability of systems of hydrodynamic type. We discuss the vanishing of the Haantjes tensor for operator fields that admit a large number of so-called conservation laws. In particular, we investigate Haantjes-zero Killing tensor fields that are associated with second-order superintegrable systems.