  Langmuir-Blodgett films (LB-films) consist from few LB-monolayers which are
high structured nanomaterials that are very promising materials for
applications. We use a geometrical approach to describe structurization into
LB-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-like
d-field) for the Lagrangian governing the 2D-motion of a particle of monolayer.
One assumed that an expansion near singular points for the constructed
geometrical Lagrangian theory describe phase transitions to LB-monolayer.
Trajectories of particles in a field of the electrocapillarity forces of
monolayer have been calculated in a resonant approximation utilizing some
Jacobi equations. A jet geometrical Yang-Mills energy is introduced and some
physical interpretations are given.
