5 papers
Fedosov manifolds with parallel symplectic Weyl curvature
Shane Rankin, Ivo Terek
A classical 1977 result by Roter states that a Riemannian manifold of dimension at least four with parallel Weyl curvature must be locally symmetric or conformally flat. We establi…
The curvature of left-invariant magnetic systems
Shane Rankin, Ivo Terek, David Weed
We compute the magnetic curvatures (in the sense of Assenza) of left-invariant magnetic systems on Lie groups and explore relations between curvature properties and algebraic prope…
Algebroid Desingularizable Poisson Structures
Shane Rankin
We introduce algebroid desingularizable Poisson manifolds, those Poisson manifolds induced by a symplectic Lie algebroid with an almost-injective anchor. This class coincides with…
The Hard Lefschetz Theorem on Kähler Lie Algebroids
Shane Rankin
Compact Kähler manifolds classically satisfy the Hard Lefschetz Theorem, which gives strong control on the underlying topology of the manifold. One expects a similar theorem to be…
Symplectic Hodge Theory on Lie Algebroids
Shane Rankin
We explore the natural analogues of the Brylinksi condition, Strong Lefschetz condition, and -lemma in Symplectic Geometry originally explored by Brylinksi, Mathieu, Yan, and G…