The Bohlin variant of the Eisenhart lift embeds Lagrangian systems into timelike geodesics of conformally flat (d+2)-dimensional metrics and yields novel examples of such metrics admitting higher-rank Killing tensors.
Goryachev-Chaplygin, Kovalevskaya, and Brdi\v{c}ka-Eardley-Nappi-Witten pp-waves spacetimes with higher rank St\"ackel-Killing tensors
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abstract
Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the Brdi\v{c}ka-Eardley-Nappi-Witten pp-waves are studied. We find out that these spacetimes possess higher rank St\"ackel-Killing tensors and that in the case of the pp-wave spacetimes the symmetry group of the St\"ackel-Killing tensors is the well-known Newton-Hooke group.
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The Bohlin variant of the Eisenhart lift
The Bohlin variant of the Eisenhart lift embeds Lagrangian systems into timelike geodesics of conformally flat (d+2)-dimensional metrics and yields novel examples of such metrics admitting higher-rank Killing tensors.