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

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The aim of this paper is to construct a canonical nonlinear connection $\Gamma =({M}_{\left(\alpha \right)\beta}^{\left(i\right)},{N}_{\left(\alpha \right)j}^{\left(i\right)})$ on the 1-jet space ${J}^{1}(T,M)$ from the Euler-Lagrange equations of the quadratic multi-time Lagrangian function $$L={h}^{\alpha \beta}\left(t\right){g}_{ij}(t,x){x}_{\alpha}^{i}{x}_{\beta}^{j}+{U}_{\left(i\right)}^{\left(\alpha \right)}(t,x){x}_{\alpha}^{i}+F(t,x)\phantom{\rule{0.166667em}{0ex}}.$$

In this paper we develop the distinguished (d-) Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures and some geometrical Maxwell-like and Einstein-like equations) for the polymomentum Hamiltonian which governs the multi-time electrodynamics.

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