  We investigate critical points and minimizers of the Yang-Mills functional YM
on quantum Heisenberg manifolds $D^c_{\mu\nu}$, where the Yang-Mills functional
is defined on the set of all compatible linear connections on finitely
generated projective modules over the QHMs. A compatible linear connection
which is both a critical point and minimizer of YM is called a Yang-Mills
connection. In this paper, we investigate Yang-Mills connections with constant
curvature. We are interested in Yang-Mills connections on the following classes
of modules over the QHMs: (i) Abadie's module $\Xi$ of trace $2\mu$ and its
submodules; (ii) modules $\Xi^\prime$ of trace $2\nu$; (iii) tensor product
modules of the form $P E^c_{\mu\nu}\otimes \Xi$, where $E^c_{\mu\nu}$ is Morita
equivalent to $D^c_{\mu\nu}$ and $P$ is a projection in $E^c_{\mu\nu}$. We
present a characterization of critical points and minimizers of YM, and provide
a class of new Yang-Mills connections with constant curvature via concrete
examples. In particular, we show that every Yang-Mills connection $\nabla$ on
$\Xi$ over $D^c_{\mu\nu}$ with constant curvature should have a certain form of
the curvature such that $\Theta_\nabla(X,Y)=\Theta_\nabla(X,Z)=0$ and
$\Theta(Y,Z)=\frac{\pi i}{\mu} Id_E$. Also we show that these Yang-Mills
connections with constant curvature do not provide global minima but only local
minima, and give two other examples which show that the critical points and
minimizers of YM depend crucially on the geometric structure of the QHMs and of
the projective modules over them. Furthermore, we construct the Grassmannian
connection on the projective modules $\Xi^\prime$ with trace $2\nu$ over the
QHMs and compute its corresponding curvature, and we construct a tensor product
connections on $P E^c_{\mu\nu}\otimes \Xi$ whose coupling constant is $2\nu$
and characterize the critical points of YM for this projective module.
