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International Journal of Mathematics and Mathematical Sciences
Volume 29, Issue 1, Pages 7-15
http://dx.doi.org/10.1155/S0161171202011018

The geometry of autonomous metrical multi-time Lagrange space of electrodynamics

Department of Mathematics I, University Politehnica of Bucharest, Splaiul Independentei, Bucharest 313-77206, Romania

Received 12 October 2000

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is to create a large geometrical background for the study of important branch of physics: electrodynamics, bosonic strings theory, magneto-hydrodynamics, and so forth. The geometrical construction is realized on the 1-jet fibre bundle J1(T,M) and is produced by a given quadratic multi-time Lagrangian function L. The Riemann-Lagrange geometry of the space EDMLpn=(J1(T,M),L), in the sense of d-connections, torsion and curvature d-tensors, allows the construction of a natural generalized multi-time field theory on EDMLPn, in the sense of generalized Maxwell and Einstein equations.