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 Staeckel 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.

References in corpus (3)

• A Recurrence Relation Approach to Higher Order Quantum Superintegrability
• Families of superintegrable Hamiltonians constructed from exceptional polynomials
• Algebraic Calculation of the Energy Eigenvalues for the Nondegenerate Three-Dimensional Kepler-Coulomb Potential

Cited by in corpus (6)

• Invariant classification of second-order conformally flat superintegrable systems
• Cylindrical type integrable classical systems in a magnetic field
• The Variety of Integrable Killing Tensors on the 3-Sphere
• Extended Hamiltonians, Coupling-Constant Metamorphosis and the Post-Winternitz System
• Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion
• Extensions of natural Hamiltonians