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

Neagu, Mircea

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From Euler-Lagrange equations to canonical nonlinear connections

Mircea Neagu (2006)

Archivum Mathematicum

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The aim of this paper is to construct a canonical nonlinear connection $Γ = (M_{(α) β}^{(i)}, N_{(α) j}^{(i)})$ on the 1-jet space $J^{1} (T, M)$ from the Euler-Lagrange equations of the quadratic multi-time Lagrangian function $L = h^{α β} (t) g_{i j} (t, x) x_{α}^{i} x_{β}^{j} + U_{(i)}^{(α)} (t, x) x_{α}^{i} + F (t, x) .$