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Geodesic equations for magnetized plasma in \(GL\)-spaces. (English) Zbl 0976.53026

Tsagas, Grigorios (ed.), Proceedings of the workshop on global analysis, differential geometry, Lie algebras, Aristotle University of Thessaloniki, Greece, October 21-25, 1996. Bucharest: Geometry Balkan Press. BSG Proc. 3, 27-34 (1999).
From the authors’ abstract: Lagrangian geometric modelling may be applied to the magnetized plasma considering the space-time manifold like a generalized Lagrange space, and hence the gravitation potentials as functions of point and direction. The purpose of our work is to determine the Lagrange geometric objects describing relativistic magnetized plasma. The elaboration of this pattern has as starting point the consideration of an energy-momentum tensor as Lagrange tensor for plasma. We accomplished a semilocal geometrization of nongravitational physical magnitudes. So, in the new space obtained by a conformal change of a metric, the movement equations of plasma become equations of the \(h\)-geodesics of the space-time, the dynamic and electromagnetic interactions being absorbed into the new geometry.
For the entire collection see [Zbl 0919.00058].

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
53B50 Applications of local differential geometry to the sciences
53C22 Geodesics in global differential geometry
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