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Langmuir-Blodgett films (LB-films) consist from few LB-monolayers which arehigh structured nanomaterials that are very promising materials forapplications. We use a geometrical approach to describe structurization intoLB-monolayers. Consequently, we develop on the 1-jet space J^1([0,\infty),R^2)the single-time Lagrange geometry (in the sense of distinguished (d-)connection, d-torsions and an abstract anisotropic electromagnetic-liked-field) for the Lagrangian governing the 2D-motion of a particle of monolayer.One assumed that an expansion near singular points for the constructedgeometrical Lagrangian theory describe phase transitions to LB-monolayer.Trajectories of particles in a field of the electrocapillarity forces ofmonolayer have been calculated in a resonant approximation utilizing someJacobi equations. A jet geometrical Yang-Mills energy is introduced and somephysical interpretations are given.

Jet theoretical Yang-Mills energy in the geometric dynamics of 2D-monolayer