Magnetic curves on flat para-K\"ahler manifolds

Authors: MOHAMED JLELI, MARIAN IOAN MUNTEANU

Abstract: In this paper we prove that spacelike and timelike magnetic trajectories corresponding to the para-K\"ahler 2-form on a para-K\"ahler manifold $(M,\p,g)$ are circles on $M$. We then classify all para-K\"ahler magnetic curves in pseudo-Euclidean spaces ${\mathbb{E}}^{2n}_n$.

Keywords: Magnetic field, para-K\"ahler manifold, circle

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