7 citations · 44 across the 10 of their papers we have counts for
10 papers
The c-projective symmetry algebras of Kähler surfaces
Gianni Manno, Jan Schumm, Andreas Vollmer
Let be a Kähler manifold with complex structure and Kähler metric . A c-projective vector field is a vector field on whose flow sends -planar curves to -planar…
3-dimensional Levi-Civita metrics with projective vector fields
Gianni Manno, Andreas Vollmer
Projective vector fields are the infinitesimal transformations whose local flow preserves geodesics up to reparametrisation. In 1882 Sophus Lie posed the problem of describing 2-di…
Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics
Andreas Vollmer
A non-degenerate second-order maximally conformally superintegrable system in dimension 2 naturally gives rise to a quadric with position dependent coefficients. It is shown how th…
Algebraic Conditions for Conformal Superintegrability in Arbitrary Dimension
Jonathan Kress, Konrad Schöbel, Andreas Vollmer
We show that the definition of a second order superintegrable system on a (pseudo-)Riemannian manifold gives rise to a conformally invariant notion of superintegrability. Conformal…
(Super-)integrable systems associated to 2-dimensional projective connections with one projective symmetry
Gianni Manno, Andreas Vollmer
Projective connections arise from equivalence classes of affine connections under the reparametrization of geodesics. They may also be viewed as quotient systems of the classical g…
Projectively equivalent 2-dimensional superintegrable systems with projective symmetries
Andreas Vollmer
This paper combines two classical theories, namely metric projective differential geometry and superintegrability. We study superintegrable systems on 2-dimensional geometries that…