  In order to use the technique of dimensional reduction, it is usually
necessary for there to be a symmetry coming from a group action. In this paper
we consider a situation in which there is no such symmetry, but in which a type
of dimensional reduction is nevertheless possible. We obtain a relation between
the Coupled Vortex equations on a closed Kahler manifold, $X$, and the
Hermitian-Einstein equations on certain $P^1$-bundles over $X$. Our results
thus generalize the dimensional reduction results of Garcia-Prada, which apply
when the Hermitian-Einstein equations are on $X\times P^1$.
