The Bohlin variant of the Eisenhart lift

2026/02/24 by Anton Galajinsky · 1 voice
Physics and Astronomy · #nlin.SI #hep-th #math-ph

paper · pdf · doi:10.1016/j.geomphys.2026.105873

arxiv published 2026/02/24 · arxiv updated 2026/05/07

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.

Citations

• Cosmological Solutions in Scalar-Tensor theory via the Eisenhart-Duval lift
• Eisenhart Lift for Scalar Fields in the FLRW Universe
• Eisenhart Lift of 2--Dimensional Mechanics
• Cosmological aspects of the Eisenhart-Duval lift
• Geometry of the isotropic oscillator driven by the conformal mode
• Black holes, hidden symmetries, and complete integrability
• Jacobi-Maupertius metric and Kepler equation
• Eisenhart lift for higher derivative systems
• Eisenhart lifts and symmetries of time-dependent systems
• Self-dual metrics with maximally superintegrable geodesic flows
• Ricci-flat spacetimes admitting higher rank Killing tensors
• Conformal Killing Tensors and covariant Hamiltonian Dynamics
• Killing tensors and canonical geometry
• Generalised Eisenhart lift of the Toda chain
• Higher rank Killing tensors and Calogero model
• Goryachev-Chaplygin, Kovalevskaya, and Brdička-Eardley-Nappi-Witten pp-waves spacetimes with higher rank Stäckel-Killing tensors
• Some Spacetimes with Higher Rank Killing-Stackel Tensors
• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Bargmann structures and Newton-Cartan theory

Discussions

• Anton Galajinsky: The Bohlin variant of the Eisenhart lift https://arxiv.org/abs/2603.15626 https://arxiv.org/pdf/2603.15626 https://arxiv.org/html/2603.15626 [bsky, 0 points, 0 comments]

Related

• Herglotz's formalism, Eisenhart lift and Killing vectors
• The Eisenhart Lift and Hamiltonian Systems
• Geodesics in the conformally flat Eisenhart metric
• Lifting the Eisenhart-Duval Lift to a Minimal Brane
• Kerr-Schild transformation of the Benenti-Francaviglia metric