Abundant Superintegrable Systems and Hessian Structures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909603819683840 |
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| author | Armstrong, John Vollmer, Andreas |
| author_facet | Armstrong, John Vollmer, Andreas |
| contents | We show that a large class of non-degenerate second-order (maximally) superintegrable systems gives rise to Hessian structures, which admit natural (Hessian) coordinates adapted to the superintegrable system. In particular, abundant superintegrable systems on Riemannian manifolds of constant sectional curvature fall into this class. We explicitly compute the natural Hessian coordinates for examples of non-degenerate second-order superintegrable systems in dimensions two and three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Abundant Superintegrable Systems and Hessian Structures Armstrong, John Vollmer, Andreas Exactly Solvable and Integrable Systems Differential Geometry 53B12, 70H33, 70H06 We show that a large class of non-degenerate second-order (maximally) superintegrable systems gives rise to Hessian structures, which admit natural (Hessian) coordinates adapted to the superintegrable system. In particular, abundant superintegrable systems on Riemannian manifolds of constant sectional curvature fall into this class. We explicitly compute the natural Hessian coordinates for examples of non-degenerate second-order superintegrable systems in dimensions two and three. |
| title | Abundant Superintegrable Systems and Hessian Structures |
| topic | Exactly Solvable and Integrable Systems Differential Geometry 53B12, 70H33, 70H06 |
| url | https://arxiv.org/abs/2410.05009 |