On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces
We prove the integrability and superintegrability of a family of natural Hamiltonians which includes and generalises those studied in some literature, originally defined on the 2D Minkowski space. Some of the new Hamiltonians are a perfect analogy of the well-known superintegrable system on the Eucl...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210698 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces. Claudia Maria Chanu and Giovanni Rastelli. SIGMA 16 (2020), 052, 16 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862699451570716672 |
|---|---|
| author | Chanu, Claudia Maria Rastelli, Giovanni |
| author_facet | Chanu, Claudia Maria Rastelli, Giovanni |
| citation_txt | On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces. Claudia Maria Chanu and Giovanni Rastelli. SIGMA 16 (2020), 052, 16 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove the integrability and superintegrability of a family of natural Hamiltonians which includes and generalises those studied in some literature, originally defined on the 2D Minkowski space. Some of the new Hamiltonians are a perfect analogy of the well-known superintegrable system on the Euclidean plane proposed by Tremblay-Turbiner-Winternitz, and they are defined on Minkowski space, as well as on all other 2D manifolds of constant curvature, Riemannian or pseudo-Riemannian. We also show how the application of the coupling-constant-metamorphosis technique allows us to obtain new superintegrable Hamiltonians from the previous ones. Moreover, for the Minkowski case, we show the quantum superintegrability of the corresponding quantum Hamiltonian operator. Our results are obtained by applying the theory of extended Hamiltonian systems, which is strictly connected with the geometry of warped manifolds.
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| first_indexed | 2025-12-17T12:04:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210698 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:31Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chanu, Claudia Maria Rastelli, Giovanni 2025-12-15T15:24:00Z 2020 On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces. Claudia Maria Chanu and Giovanni Rastelli. SIGMA 16 (2020), 052, 16 pages 1815-0659 2020 Mathematics Subject Classification: 37J35; 70H33 arXiv:2001.08613 https://nasplib.isofts.kiev.ua/handle/123456789/210698 https://doi.org/10.3842/SIGMA.2020.052 We prove the integrability and superintegrability of a family of natural Hamiltonians which includes and generalises those studied in some literature, originally defined on the 2D Minkowski space. Some of the new Hamiltonians are a perfect analogy of the well-known superintegrable system on the Euclidean plane proposed by Tremblay-Turbiner-Winternitz, and they are defined on Minkowski space, as well as on all other 2D manifolds of constant curvature, Riemannian or pseudo-Riemannian. We also show how the application of the coupling-constant-metamorphosis technique allows us to obtain new superintegrable Hamiltonians from the previous ones. Moreover, for the Minkowski case, we show the quantum superintegrability of the corresponding quantum Hamiltonian operator. Our results are obtained by applying the theory of extended Hamiltonian systems, which is strictly connected with the geometry of warped manifolds. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces Article published earlier |
| spellingShingle | On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces Chanu, Claudia Maria Rastelli, Giovanni |
| title | On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces |
| title_full | On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces |
| title_fullStr | On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces |
| title_full_unstemmed | On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces |
| title_short | On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces |
| title_sort | on the extended-hamiltonian structure of certain superintegrable systems on constant-curvature riemannian and pseudo-riemannian surfaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210698 |
| work_keys_str_mv | AT chanuclaudiamaria ontheextendedhamiltonianstructureofcertainsuperintegrablesystemsonconstantcurvatureriemannianandpseudoriemanniansurfaces AT rastelligiovanni ontheextendedhamiltonianstructureofcertainsuperintegrablesystemsonconstantcurvatureriemannianandpseudoriemanniansurfaces |