  We characterize those closed $2k$-manifolds admitting smooth maps into
$(k+1)$-manifolds with only finitely many critical points, for $k\in\{2,4\}$.
We compute then the minimal number of critical points of such smooth maps for
$k=2$ and, under some fundamental group restrictions, also for $k=4$. The main
ingredients are King's local classification of isolated singularities,
decomposition theory, low dimensional cobordisms of spherical fibrations and
3-manifolds topology.
