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EnglishWe consider the anti-de Sitter space $H_3^1$ and the hyperbolic Hopf fibration $h : H_3^1 (1) \to H_2(1\2)$. 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.
| Titolo: | Hopf magnetic curves in the anti-de Sitter space ℍ31 |
| Autori: | |
| Data di pubblicazione: | 2018 |
| Rivista: | |
| Abstract: | We consider the anti-de Sitter space $H_3^1$ and the hyperbolic Hopf fibration $h : H_3^1 (1) \to H_2(1\2)$. 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. |
| Handle: | http://hdl.handle.net/11587/427126 |
| Appare nelle tipologie: | Articolo pubblicato su Rivista |
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