Dynamics of particle systems and kinetic equations in Weyl geometry space

The basic properties of the Weyl geometry, which generalizes the space-time geometry of the General Theory of Relativity, are described. It is shown that particle dynamics in Weyl space can be formulated in terms of Lagrangian geometry. A method for constructing kinetic equations in Weyl space is considered, and their connections with equations of Lagrangian manifolds is established.