We present unique solutions of the Seiberg-Witten monopole equations in which the U (1) curvature is covariantly constant, the monopole Weyl spinor consists of a single constant component and the 4-manifold is a product of two Riemann surfaces of genuses p ₁ and p ₂ . There are p ₁ -1 magnetic vortices on one surface and p ₂ -1 electric ones on the other, with p ₁ +p ₂ 2 (p ₁ = p ₂ = 1 being excluded). When p ₁ = p ₂ , the electromagnetic fields are self-dual and one also has a solution of the coupled Euclidean Einstein-Maxwell-Dirac equations, with the monopole condensate serving as a cosmological constant. The metric is decomposable and the electromagnetic fields are covariantly constant as in the Bertotti-Robinson solution. The Einstein metric can also be derived from a Kähler potential satisfying the Monge-Ampère equations.