The Bohlin variant of the Eisenhart lift
Exactly Solvable and Integrable Systems
2026-05-08 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
Inspired by the Bohlin transformation relating the planar harmonic oscillator to the Kepler problem, a variant of the Eisenhart lift is studied, in which a Lagrangian conservative dynamical system with d degrees of freedom is embedded into timelike geodesics of a conformally flat metric on a (d+2)-dimensional space-time of the Lorentzian signature. The uplift is used to construct novel examples of conformally flat metrics admitting higher rank Killing tensors.
Keywords
Cite
@article{arxiv.2603.15626,
title = {The Bohlin variant of the Eisenhart lift},
author = {Anton Galajinsky},
journal= {arXiv preprint arXiv:2603.15626},
year = {2026}
}
Comments
v2: 13 pages, minor improvements, the version to appear in J. Geom. Phys