  In present paper we confirm our previous result [5] that the Planck constant
is adiabatic invariant of electromagnetic field propagating on the
adiabatically changed Finslerian manifold. Direct calculation from cosmological
parameters gives value h=6x10(-27) (erg s). We also confirm that Planck
constant (and hence other fundamental constants which depend on h) is varied on
time due to changing of geometry.
  As an example the variation of the fine structure constant is calculated. Its
relative variation ((da/dt)/a) consist 1.0x10(-18) (1/s).
  We show that on the Finsler manifold characterized by adiabatically changed
geometry, classical free electromagnetic field is quantized geometrically, from
the properties of the manifold in such manner that adiabatic invariant of field
is ET=6x10(-27)=h(erg s).
  Equations of electrodynamics on the Finslerian manifold are suggested. It is
stressed that quantization naturally appears from these equations and is
provoked by adiabatically changed geometry of manifold. We consider in details
two direct consequences of the equations: i) cosmological redshift of photons
and ii) effects of Aharonov -- Bohm that immediately follow from obtained
equations. It is shown that quantization of system consists of electromagnetic
field and baryonic components (like atoms) is obvious and has clear
explanation.
