Year: 2024
Type: article
Abstract: Second‐order (maximally) conformally superintegrable systems play an important role as models of mechanical systems, including systems such as the Kepler–Coulomb system and the isotropic harmonic oscillator. This paper is dedicated to understanding non‐ and semi‐degenerate systems. We obtain “projective flatness” results for two torsion‐free connections naturally associated to such systems. This viewpoint sheds some light onto the interrelationship of properly and conformally (second‐order maximally) superintegrable systems from a geometrical perspective. It is shown that the semi‐degenerate secondary structure tensor can be viewed as the Ricci curvature of a natural torsion‐free connection defined by the primary structure tensor (and similarly in the non‐degenerate case). It is also shown that properly semi‐degenerate systems are characterised, similar to the non‐degenerate case, by the vanishing of the secondary structure tensor.
DOI: 10.1112/blms.13213
Author: Andreas Vollmer
Institution: Universität Hamburg
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,780
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4405758697