  It is shown that in the spin-charge-family theory, as well as in all the
Kaluza-Klein like theories, vielbeins and spin connections manifest in
$d=(3+1)$ space equivalent vector gauge fields, when space with $d\ge5$
manifests large enough symmetry. The authors demonstrate this equivalence in
spaces with the symmetry of the metric tensor in the space out of $d=(3+1)$ -
$g^{\sigma \tau} = \eta^{\sigma \tau} \,f^{2}$ - for any scalar function $f$ of
the coordinates $x^{\sigma}$, where $x^{\sigma}$ denotes coordinates of space
out of $d=(3+1)$. Also the connection between vielbeins and scalar gauge fields
in $d=(3+1)$ (offering the explanation for the Higgs's scalar) is discussed.
