Address.
Str. Lamaitei, Nr. 66, Bl. 93, Sc. G, Ap. 10, Brasov, BV
500371, Romania
E-mail. mirceaneagu73@yahoo.com
Abstract.
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
$$L=h^{\alpha \beta }(t)g_{ij}(t,x)x_{\alpha }^{i}x_{\beta}^{j}+U_{(i)}^{(\alpha )}(t,x)x_{\alpha }^{i}+F(t,x)\,.$$
AMSclassification. 53B40, 53C60, 53C80.
Keywords. 1-jet fibre bundles, nonlinear connections, quadratic Lagrangian functions.