The Bohlin variant of the Eisenhart lift
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915985646157824 |
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| author | Galajinsky, Anton |
| author_facet | Galajinsky, Anton |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15626 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Bohlin variant of the Eisenhart lift Galajinsky, Anton Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics 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. |
| title | The Bohlin variant of the Eisenhart lift |
| topic | Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2603.15626 |