  We introduce and study two classes of Hubbard models with magnetic flux or
with spin-orbit coupling, which have a flat lowest band separated from other
bands by a nonzero gap. We study the Chern number of the flat bands, and find
that it is zero for the first class but can be nontrivial in the second. We
also prove that the introduction of on-site Coulomb repulsion leads to
ferromagnetism in both the classes.
