Hopf magnetic curves in the anti-de Sitter space 13

We consider the anti-de Sitter space H 3 1 and the hyperbolic Hopf fibration h : H 3 1 (1) → H 2 (1/2).Using their description in terms of paraquaternions, we study the magnetic curves of the hyperbolic Hopf vector field.A complete classification is obtained for light-like magnetic curves, showing in particular the existence of periodic examples, and emphasizing their relationship with the hyperbolic Hopf fibration.Finally, we give a new interpretation of magnetic curves in H 3 1 using some techniques of Lie groups and Lie algebras.