Separation of Variables and Superintegrability on Riemannian Coverings
We introduce Stäckel separable coordinates on the covering manifolds 𝑀ₖ, where 𝑘 is a rational parameter, for certain constant-curvature Riemannian manifolds with a warped manifold structure. These covering manifolds appear implicitly in the literature as connected with superintegrable systems with...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212022 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Separation of Variables and Superintegrability on Riemannian Coverings. Claudia Maria Chanu and Giovanni Rastelli. SIGMA 19 (2023), 062, 18 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We introduce Stäckel separable coordinates on the covering manifolds 𝑀ₖ, where 𝑘 is a rational parameter, for certain constant-curvature Riemannian manifolds with a warped manifold structure. These covering manifolds appear implicitly in the literature as connected with superintegrable systems with polynomial momenta first integrals of arbitrarily high degree, such as the Tremblay-Turbiner-Winternitz system. We study here for the first time the multiseparability and superintegrability of natural Hamiltonian systems on these manifolds and see how these properties depend on the parameter 𝑘.
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| ISSN: | 1815-0659 |