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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 bundleJ1(T,M)and is produced by a given quadratic multi-time Lagrangian functionL. The Riemann-Lagrange geometry of the spaceEDMLpn=(J1(T,M),L), in the sense ofd-connections, torsion and curvatured-tensors, allows the construction of a naturaldoi:10.1155/s0161171202011018 fatcat:wp7u6qhjt5funea3shunrj4oai