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Separation of Variables and Superintegrability on Riemannian Coverings
Claudia Maria Chanua, Giovanni Rastellib a Dipartimento di Scienze Umane e Sociali, Università della Valle d’Aosta, Italy
b Dipartimento di Matematica, Università di Torino, Italy
Abstract:
We introduce Stäckel separable coordinates on the covering manifolds $M_k$, where $k$ is a rational parameter, of certain constant-curvature Riemannian manifolds with the structure of warped manifold. These covering manifolds appear implicitly in literature as connected with superintegrable systems with polynomial in the momenta first integrals of arbitrarily high degree, such as the Tremblay–Turbiner–Winternitz system. We study here for the first time multiseparability and superintegrability of natural Hamiltonian systems on these manifolds and see how these properties depend on the parameter $k$.
Keywords:
Riemannian coverings, integrable systems, separable coordinates.
Received: January 11, 2023; in final form August 23, 2023; Published online September 3, 2023
Citation:
Claudia Maria Chanu, Giovanni Rastelli, “Separation of Variables and Superintegrability on Riemannian Coverings”, SIGMA, 19 (2023), 062, 18 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1957 https://www.mathnet.ru/eng/sigma/v19/p62
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Abstract page: | 37 | Full-text PDF : | 5 | References: | 7 |
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