  We present a geometrical unification theory in a Kaluza-Klein approach that
achieve the geometrization of a generic gauge theory bosonic component.
  We show how it is possible to derive the gauge charge conservation from the
invariance of the model under extra-dimensional translations and to geometrize
gauge connections for spinors, thus we can introduce the matter just by free
spinorial fields. Then, we present the applications to i)a pentadimensional
manifold $V^{4}\otimes S^{1}$, so reproducing the original Kaluza-Klein theory,
unless some extensions related to the rule of the scalar field contained in the
metric and the introduction of matter by spinors with a phase dependence from
the fifth coordinate, ii)a seven-dimensional manifold $V^{4}\otimes
S^{1}\otimes S^{2}$, in which we geometrize the electro-weak model by
introducing two spinors for any leptonic family and quark generation and a
scalar field with two components with opposite hypercharge, responsible of
spontaneous symmetry breaking.
