| Résume | We introduce a system of differential equations coupling a Hermitian metric on a holomorphic vector bundle over a compact complex manifold and a Kähler metric on the manifold. We then study invariant solutions under the action of the group of rotations on the product of the Riemann sphere and a compact Riemann surface. This leads to the gravitating vortex equations, whose existence of solutions, relating in particular to Mumford’s Geometric Invariant Theory, is discussed |
