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Motion of charged particles in two-step nilpotent Lie groups. (English) Zbl 1216.53022

Summary: We formulate the equation of motion of a charged particle in a Riemannian manifold with a closed two form. Since a two-step nilpotent Lie group has natural left-invariant closed two forms, it is natural to consider the motion of a charged particle in a simply connected two-step nilpotent Lie group with left invariant metric. We study the behavior of the motion of a charged particle in the above spaces.

MSC:

53B20 Local Riemannian geometry
70B05 Kinematics of a particle
53C30 Differential geometry of homogeneous manifolds
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