Abstract
In this paper we classify magnetic trajectories γ in \({{\mathbb{R}}^{2N+1}}\) endowed with a canonical quasi-Sasakian structure, corresponding to a magnetic field proportional to the fundamental 2-form. We prove that they are helices of order 5 and we show that there exists a totally geodesic \({{\mathbb{R}}^5}\) in \({\mathbb{R}^{2N+1}}\) such that γ lies in \({{\mathbb{R}}^5}\). Moreover, the quasi-Sasakian structure of \({{\mathbb{R}}^5}\) is that induced from the ambient manifold.
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Jleli, M., Munteanu, M.I. & Nistor, A.I. Magnetic Trajectories in an Almost Contact Metric Manifold \({\mathbb{R}^{2N+1}}\) . Results. Math. 67, 125–134 (2015). https://doi.org/10.1007/s00025-014-0398-y
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DOI: https://doi.org/10.1007/s00025-014-0398-y