Geometric objects defined by almost Lie structures (Q2782573)

The aim of this paper is to extend some classical geometric objects, associated with Lagrange and Hamilton metrics on manifolds, to vector bundles endowed with an almost Lie structure (ALS), defined by one of the authors [\textit{P. Popescu}, Rev. Roum. Math. Pures Appl. 37, 779-789 (1992; Zbl 0774.53017)]. One defines and studies for an ALS linear and nonlinear connections associated with a Lagrangian or a Hamiltonian, semi-sprays, Legendre transformations and Lagrange equations.NEWLINENEWLINENEWLINEFinally, one extends to an ALS the Theorem of Ambrose-Palais-Singer concerning the existence of a linear connection having a given spray as the geodesic one.NEWLINENEWLINEFor the entire collection see [Zbl 0980.00030].