Abundant Superintegrable Systems and Hessian Structures
arXiv:2410.05009 · doi:10.1016/j.geomphys.2025.105503
Abstract
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.
arXiv comment15 pages
References in corpus (8)
- An elementary introduction to information geometry
- Completeness of superintegrability in two-dimensional constant curvature spaces
- Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials
- Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere
- Invariant classification of second-order conformally flat superintegrable systems
- An Algebraic Geometric Foundation for a Classification of Superintegrable Systems in Arbitrary Dimension
- Algebraic Conditions for Conformal Superintegrability in Arbitrary Dimension
- Torsion-free connections of second-order maximally superintegrable systems