  We establish relations which express the generalized parton distributions
(GPDs) describing the $N\to \Delta$ transition in terms of the nucleon GPDs.
These relations are based on the known large-$N_c$ relation between the $N\to
\Delta$ electric quadrupole moment and the neutron charge radius, and a newly
derived large-$N_c$ relation between the electric quadrupole ($E2$) and Coulomb
quadrupole ($C2$) transitions. Namely, in the large-$N_c$ limit we find
$C2=E2$. The resulting relations among the nucleon and $N\to\Delta$ GPDs
provide predictions for the $N\to\Delta$ electromagnetic form factors which are
found to be in very good agreement with experiment for moderate momentum
transfers.
