Dimensional reduction of the perturbed Hermitian-Einstein equation
  Given a Kaehlerian holomorphic fiber bundle whose fiber is a compact homogeneous Kaehler manifold, we describe the perturbed Hermitian-Einstein equations relative to certain holomorphic vector bundles. With respect to special metrics on the holomorphic bundles, there is a dimensional reduction procedure which reduces these equations to a system of equations on the base, known as the twisted coupled vortex equations. 
Steven B. Bradlow, James F. Glazebrook and Franz W. Kamber