VORTICES IN CURVED SPACE-TIME

We study an Abelian Higgs model coupled to a background metric. We find Bogomol'nyi equations when the coupling is achieved through an R phi(2) term (R being the scalar curvature and phi the Higgs scaler). Remarkably, these equations coincide with those arising in models where the gauge field dynamics is governed by a Chern-Simons term so that vortex solutions in our system can be related to self-dual Chern-Simons vortices.