  In this paper, we discuss the Yang-Mills functional and a certain family of
its critical points on quantum Heisenberg manifolds using noncommutative
geometrical methods developed by A. Connes and M. Rieffel. In our main result,
we construct a certain family of connections on a projective module over a
quantum Heisenberg manifold that give rise to critical points of the Yang-Mills
functional. Moreover, we show that this set of solutions can be described as a
set of solutions to Laplace's equation on quantum Heisenberg manifolds.
