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On dual-projectively equivalent connections associated to second order superintegrable systems
Andreas Vollmer
Pre-geodesics of an affine connection are the curves that are geodesics after a reparametrization (the analogous concept in Kähler geometry is known as J-planar curves). Similarly,…
Second-order superintegrable systems and Weylian geometry
Andreas Vollmer
Abundant second-order maximally conformally superintegrable Hamiltonian systems are re-examined, revealing their underlying natural Weyl structure and offering a clearer geometric…
Superintegrable systems on conformal surfaces
Jonathan Kress, Konrad Schöbel, Andreas Vollmer
We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors,…
Torsion-free connections of second-order maximally superintegrable systems
Andreas Vollmer
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 iso…