Vortices over Riemann surfaces and dominated splittings

Abstract We associate a flow $\phi $ with solution of the vortex equations on closed oriented Riemannian 2-manifold $(M,g)$ negative Euler characteristic and investigate its properties. show that always admits dominated splitting identify special cases in which is Anosov. In particular, starting from holomorphic differentials fractional degree, we produce novel examples Anosov flows suitable roots unit tangent bundle .