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Superintegrability in a non-conformally-flat space
Abstract
Superintegrable systems in two- and three-dimensional spaces of constant curvature have been extensively studied. From these, superintegrable systems in conformally flat spaces can be constructed by Stackel transform. In this paper a method developed to establish the superintegrability of the Tremblay-Turbiner-Winternitz system in two dimensions is extended to higher dimensions and a superintegrable system on a non-conformally-flat four-dimensional space is found. In doing so, curvature corrections to the corresponding classical potential are found to be necessary. It is found that some subalgebras of the symmetry algebra close polynomially.
Type
Journal Article
Type of thesis
Series
Citation
Kalnins, E. G., Kress, J. M., & Miller, W. (2013). Superintegrability in a non-conformally-flat space. Journal of Physics A: Mathematical and Theoretical, 46(2), 022002.
Date
2013
Publisher
Institute of Physics