The Bohlin variant of the Eisenhart lift
arXiv:2603.15626 · doi:10.1016/j.geomphys.2026.105873
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.
arXiv commentv2: 13 pages, minor improvements, the version to appear in J. Geom. Phys
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