Integrable magnetic geodesic flows on Lie groups

Abstract

Right-invariant geodesic flows on manifolds of Lie groups associated with 2-cocycles of corresponding Lie algebras are discussed. Algebra of integrals of motion for magnetic geodesic flows is considered and necessary and sufficient condition of integrability in quadratures is formulated. Canonic forms for 2-cocycles of all 4-dimensional Lie algebras are given and integrable cases among them are separated.

16 pages

References in corpus (1)

• Magnetic Geodesic Flows on Coadjoint Orbits

Cited by in corpus (8)

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• Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions
• Contact magnetic geodesic and sub-Riemannian flows on $V_{n,2}$ and integrable cases of a heavy rigid body with a gyrostat