International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 1, Pages 7-15
doi: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 Mircea Neagu. 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.