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Meeting ID: 824 333 6174
Speaker: V. Assenza (Heidelberg, Germany)
Time: April 25, 2022 (17:00 Beijing time, 16:00 Novosibirsk time).
Abstract: A Magnetic System describes the motion of a charged particle moving on a Riemannian Manifold under the influence of a magnetic field. Trajectories for this dynamics are called Magnetic Geodesics and one of the main tasks in the theory is to investigate the existence of Magnetic Geodesic which are closed. In general, this depends on the magnetic system taken into account and on the topology of the base space. Inspired by the work of Bahri and Taimanov, I will introduce the notion of Magnetic Curvature which is a perturbation of the standard Riemannian curvature due to the magnetic interaction. We will see that Closed Magnetic Geodesic exists when the Magnetic Curvature is positive which happens, for instance, when the magnetic field is sufficiently strong.