  In this work we develop a geometrical unification theory for gravity and the
electro-weak model in a Kaluza-Klein approach; in particular, from the
curvature dimensional reduction Einstein-Yang-Mills action is obtained. We
consider two possible space-time manifolds: 1)$V^{4}\otimes S^{1}\otimes S^{2}$
where isospin doublets are identified with spinors; 2) $V^{4}\otimes
S^{1}\otimes S^{3}$ in which both quarks and leptons doublets can be recast
into the same spinor, such that the equal number of quark generations and
leptonic families is explained. Finally a self-interacting complex scalar field
is introduced to reproduce the spontaneous symmetry breaking mechanism; in this
respect, at the end we get an Higgs fields whose two components have got
opposite hypercharges.
