New aspects of lagrangian relativity

The geometry of Lagrange spaces is applied to the description of classical general relativity and electrodynamics. First the Einstein equations are given in a new form, where the geometrical objects related to the internal variables are separated from those related to the external variables. After this, several special Lagrange spaces are analyzed. The almost Riemannian Lagrange spaces are rather simple for explicit calculations, and they recover all classical results of general relativity and electrodynamics. Further, the almost locally Minkowski Lagrange spaces and the almost Finsler Lagrage spaces are discussed. Although the latter are complicated from the geometrical point of view, they are interesting candidates for physical interpretations.