On Haantjes tensors for second-order superintegrable systems

2024/12/17 by Ian Marquette, Marquette, Ian, D. McLeod +5 · 1 citation
Engineering · Physics and Astronomy · #37J35 #70H06 #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Particle accelerators and beam dynamics #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2412.13007

openalex publication_date 2024/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Stäckel and Eisenhart lifts, Haantjes geometry and Gravitation

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