Magnetic curves on cotangent bundles endowed with the Riemann extension
Volume 168 / 2022
Colloquium Mathematicum 168 (2022), 47-58
MSC: Primary 53C22, 53C25, 53C15; Secondary 53C80.
DOI: 10.4064/cm7924-12-2020
Published online: 9 September 2021
Abstract
The Riemann extension on the phase space (which goes back to Patterson, Walker, and Willmore) was generalized by Kowalski and Sekizawa to the natural Riemann extension, which is also a semi-Riemannian metric of neutral signature. With respect to this metric we find all geodesics and magnetic curves which are integral curves of the vector fields on the phase space, obtained by using vertical and complete lifts. This study is then done on all level hypersurfaces of the phase space.
