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.
