6 papers
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…
Finiteness of Totally Magnetic Hypersurfaces
James Marshall Reber, Ivo Terek
By introducing a dynamical version of the second fundamental form, we generalize a recent result of Filip-Fisher-Lowe to the setting of magnetic systems. Namely, we show that a rea…
The submanifold compatibility equations in magnetic geometry
Ivo Terek
With the notions of magnetic curvature and magnetic second fundamental form recently introduced by Assenza and Albers-Benedetti-Maier, respectively, we establish analogues of the G…
Parallel differential forms of codegree two, and three-forms in dimension six
Andrzej Derdzinski, Paolo Piccione, Ivo Terek
For a differential form on a manifold, having constant components in suitable local coordinates trivially implies being parallel relative to a torsion-free connection, and the conv…
Magnetic flatness and E. Hopf's theorem for magnetic systems
Valerio Assenza, James Marshall Reber, Ivo Terek
Using the notion of magnetic curvature recently introduced by the first author, we extend E. Hopf's theorem to the setting of magnetic systems. Namely, we prove that if the magneti…
Marked length spectrum rigidity for Anosov magnetic surfaces
Valerio Assenza, Jacopo de Simoi, James Marshall Reber +1
We show that if is a closed, connected, oriented surface, and two Anosov magnetic systems on are conjugate by a volume-preserving conjugacy isotopic to the identity, with t…