Comment on: "St\"{a}ckel and Eisenhart lifts, Haantjes geometry and Gravitation"

TL;DR

This paper discusses the reinterpretation of Jacobi's classical method for integrable Hamiltonian systems through Stäckel lifts and Haantjes geometry, clarifying potential confusions in recent presentations.

Contribution

It clarifies the relationship between Jacobi's method, Stäckel lifts, and Haantjes geometry, providing insights into their connections in integrable systems.

Findings

Reinterpretation of Jacobi's method in modern geometric terms

Clarification of the relationship between Stäckel lifts and Haantjes geometry

Potential resolution of confusion in recent literature

Abstract

One of the oldest methods for constructing integrable Hamiltonian systems, proposed by Jacobi, recently is being presented as a novel St\"{a}ckel lift construction related with Haantjes geometry. It may cause some confusion.