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

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.