  The non-Abelian Kaluza-Klein unification of gravitation with gauge fields
theory is reformulated, with the inclusion of a massive spin-2 field defined by
the extrinsic curvature. The internal space is non-compact, characterized by
the group of rotations of vectors orthogonal to the space-time. The
non-compactness of the internal space warrants the solution of the fermion
chirality problem of the original Kaluza-Klein theory and makes it closer to
the more recent Brane World paradigm, in special to the so called DGP model.
However, the access of gravitation to the extra dimensions is defined by the
mentioned massive spin-2 field obeying the Fierz-Pauli equation. The existence
of a short range gravitational component makes possible to apply the modified
Kaluza-Klein unification to the Tev scale of energies.
