Dimensional Reduction of the Perturbed Hermitian–einstein Equation

Given a Kählerian holomorphic fiber bundle F →֒ M → X, whose fiber F is a compact homogeneous Kähler manifold, we describe the perturbed Hermitian–Einstein equations relative to certain holomorphic vector bundles E → M . With respect to special metrics on E, there is a dimensional reduction procedure which reduces this equation to a system of equations on X known as the twisted coupled vortex equations.