One of the Helmholtz conditions for the inverse problem of a Lagrangian Mechanics is the metric compatibility of a semispray and the associated nonlinear connection with a generalized Lagrange metric. In this paper, with respect to the supermetric induced by the Hessian of the Lagrangian, we find a family of nonlinear connections compatible with supermetric. In a particular case, when a Lagrangian superfunction is regular, we have a solution for the Euler-Lagrange superequation which defines a metric nonlinear connection.
Azizpour, E. (2023). On the compatibility of supermetrics with nonlinear connections. Journal of Finsler Geometry and its Applications, 4(2), 22-37. doi: 10.22098/jfga.2023.13513.1094
MLA
Esmaeil Azizpour. "On the compatibility of supermetrics with nonlinear connections". Journal of Finsler Geometry and its Applications, 4, 2, 2023, 22-37. doi: 10.22098/jfga.2023.13513.1094
HARVARD
Azizpour, E. (2023). 'On the compatibility of supermetrics with nonlinear connections', Journal of Finsler Geometry and its Applications, 4(2), pp. 22-37. doi: 10.22098/jfga.2023.13513.1094
VANCOUVER
Azizpour, E. On the compatibility of supermetrics with nonlinear connections. Journal of Finsler Geometry and its Applications, 2023; 4(2): 22-37. doi: 10.22098/jfga.2023.13513.1094
)