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An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow Fontana McNally, Josep Miranda Galcerán, Eva Peralta Salas, Daniel Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions Àrees temàtiques de la UPC::Matemàtiques i estadística Contact geometry Reeb vector field Beltramivector field Euler equations Lifted metric Classificació AMS::34 Ordinary differential equations Classificació AMS::51 Geometry © 2024 The Authors. Published by the Royal Society under the terms of theCreative Commons Attribution Licensehttp://creativecommons.org/licenses/by/4.0/ We prove that the correspondence between Reeb and Beltrami vector fields presented in Etnyre & Ghrist (Etnyre, Ghrist 2000 Nonlinearity 13, 441–458 (doi:10.1088/0951-7715/13/2/306)) can be made equivariant whenever additional symmetries of the underlying geometric structures are considered. As a corollary of this correspondence, we show that energy levels above the maximum of the potential energy of mechanical Hamiltonian systems can be viewed as stationary fluid flows, though the metric is not prescribed. In particular, we showcase the emblematic example of the n-body problem and focus on the Kepler problem. We explicitly construct a compatible Riemannian metric that makes the Kepler problem of celestial mechanics a stationary fluid flow (of Beltrami type) on a suitable manifold, the Kepler–Euler flow. Peer Reviewed Postprint (author's final draft) 2024-01-31 Article Fontana, J.; Miranda, E.; Peralta, D. An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow. "Proceedings - Royal Society. Mathematical, physical and engineering sciences", 31 Gener 2024, vol. 480, núm. 2282, article 20230499, p. 1-16. 1471-2946 https://hdl.handle.net/2117/406801 10.1098/rspa.2023.0499 eng https://royalsocietypublishing.org/doi/10.1098/rspa.2023.0499 http://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access Attribution-NonCommercial-NoDerivatives 4.0 International 16 p. application/pdf Royal Society