  It is known that the almost-Kaehler anti-self-dual metrics on a given
4-manifold sweep out an open subset in the moduli space of anti-self-dual
metrics. However, we show here by example that this subset is not generally
closed, and so need not sweep out entire connected components in the moduli
space. Our construction hinges on an unexpected link between harmonic functions
on certain hyperbolic 3-manifolds and self-dual harmonic 2-forms on associated
4-manifolds.
