On some Closed Magnetic Curves on a 3-torus

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Abstract

We consider two magnetic fields on the 3-torus obtained from two different contact forms on the Euclidean 3-space and we study when their corresponding normal magnetic curves are closed. We obtain periodicity conditions analogues to those for the closed geodesics on the torus.

Keywords

Magnetic field Closed curve Periodicity Elliptic function 

Mathematics Subject Classification (2010)

53C15 53C25 37J45 37C27 53C80 

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Faculty of MathematicsAlexandru Ioan Cuza University of IaşiIaşiRomania
  2. 2.Department of Mathematics and InformaticsGh. Asachi Technical University of IaşiIasiRomania

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