Local product structure for equilibrium states of geodesic flows and applications

Let $ S $ be a compact surface of genus $ \geq 2 $ equipped with a metric that is flat everywhere except at finitely many cone points with angles greater than $ 2\pi $. We examine the geodesic flow on $ S $ and prove local product structure for a wide class of equilibrium states. Using this, we establish the Bernoulli property for these systems. We also establish local product structure for a similar class of equilibrium states for geodesic flows on rank 1, nonpositively curved manifolds.