  D. D. Long and A. W. Reid have shown that some compact flat 3-manifold cannot
be diffeomorphic to a cusp cross-section of any complete finite volume 1-cusped
real hyperbolic 4-manifold. This note concerns the complex hyperbolic case. We
give a negative answer that there exists a 3-dimensional closed Heisenberg
infranilmanifold which cannot be diffeomorphic to a cusp cross-section of any
complete finite volume 1-cusped complex hyperbolic 2-manifold.
