Separation of Variables and Superintegrability on Riemannian Coverings
We introduce Stäckel separable coordinates on the covering manifolds ₖ, where 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 po...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2023 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212022 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Separation of Variables and Superintegrability on Riemannian Coverings. Claudia Maria Chanu and Giovanni Rastelli. SIGMA 19 (2023), 062, 18 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862609178649952256 |
|---|---|
| author | Chanu, Claudia Maria Rastelli, Giovanni |
| author_facet | Chanu, Claudia Maria Rastelli, Giovanni |
| citation_txt | Separation of Variables and Superintegrability on Riemannian Coverings. Claudia Maria Chanu and Giovanni Rastelli. SIGMA 19 (2023), 062, 18 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We introduce Stäckel separable coordinates on the covering manifolds ₖ, where 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 .
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| first_indexed | 2026-03-14T05:53:22Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212022 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T05:53:22Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chanu, Claudia Maria Rastelli, Giovanni 2026-01-22T09:21:51Z 2023 Separation of Variables and Superintegrability on Riemannian Coverings. Claudia Maria Chanu and Giovanni Rastelli. SIGMA 19 (2023), 062, 18 pages 1815-0659 2020 Mathematics Subject Classification: 70H06; 58J60 arXiv:2208.12690 https://nasplib.isofts.kiev.ua/handle/123456789/212022 https://doi.org/10.3842/SIGMA.2023.062 We introduce Stäckel separable coordinates on the covering manifolds ₖ, where 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 . The authors wish to thank Manuele Santoprete for useful discussions about the topic of this article, and the anonymous referees for their valuable suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Separation of Variables and Superintegrability on Riemannian Coverings Article published earlier |
| spellingShingle | Separation of Variables and Superintegrability on Riemannian Coverings Chanu, Claudia Maria Rastelli, Giovanni |
| title | Separation of Variables and Superintegrability on Riemannian Coverings |
| title_full | Separation of Variables and Superintegrability on Riemannian Coverings |
| title_fullStr | Separation of Variables and Superintegrability on Riemannian Coverings |
| title_full_unstemmed | Separation of Variables and Superintegrability on Riemannian Coverings |
| title_short | Separation of Variables and Superintegrability on Riemannian Coverings |
| title_sort | separation of variables and superintegrability on riemannian coverings |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212022 |
| work_keys_str_mv | AT chanuclaudiamaria separationofvariablesandsuperintegrabilityonriemanniancoverings AT rastelligiovanni separationofvariablesandsuperintegrabilityonriemanniancoverings |