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Keywords:
1-jet fibre bundles; nonlinear connections; quadratic Lagrangian functions
1-jet fibre bundles; nonlinear connections; quadratic Lagrangian functions
Summary:
The aim of this paper is to construct a canonical nonlinear connection $\Gamma =(M_{(\alpha )\beta }^{(i)}, N_{(\alpha )j}^{(i)})$ on the 1-jet space $J^{1}(T,M)$ from the Euler-Lagrange equations of the quadratic multi-time Lagrangian function \[ L=h^{\alpha \beta }(t)g_{ij}(t,x)x_{\alpha }^{i}x_{\beta }^{j}+U_{(i)}^{(\alpha )}(t,x)x_{\alpha }^{i}+F(t,x)\,. \]
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