• DOI:10.1063/1.4975339
• Corpus ID: 119568214

Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability

@article{Cariena2017SuperintegrableSO,
  title={Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability},
  author={Jos{\'e} F. Cari{\~n}ena and Francisco J. Herranz and Manuel F Ra{\~n}ada},
  journal={Journal of Mathematical Physics},
  year={2017},
  volume={58},
  pages={022701}
}

• J. Cariñena, F. J. Herranz, M. F. Rañada
• Published 20 January 2017
• Mathematics
• Journal of Mathematical Physics

The Eisenhart geometric formalism, which transforms an Euclidean natural Hamiltonian H = T + V into a geodesic Hamiltonian T with one additional degree of freedom, is applied to the four families of quadratically superintegrable systems with multiple separabilities in the Euclidean plane. First, the separability and superintegrability of such four geodesic Hamiltonians T r (r = a, b, c, d) in a three-dimensional curved space are studied and then these four systems are modified with the addition of a potential U r leading to H r = T r + U r . Second, we study the superintegrability of the four Hamiltonians H ˜ r = H r / μ r , where μr is a certain position-dependent mass that enjoys the same separability as the original system H r . All the Hamiltonians here studied describe superintegrable systems on non-Euclidean three-dimensional manifolds with a broken spherical symmetry.