Previous studies have shown considerable discrepancies in the characteristics of pedestrian flow obtained in different experiments. So far, the origin of these discrepancies is not well understood. Here we test a possible mechanism by studying the possible influence of geometry on pedestrian traffic by controlled experiments in different set-ups. By combining instantaneous and improved local measurements we find strong indications for an influence of curvature on the flow properties comparing local flows and densities for an oval set-up, which includes a straight part, and a circular set-up. In the jamming phase, the most efficient flow appears in the straight passage (curvature K=0) where the flow is about 20% higher than in the curved parts. We relate this reduction of flow in the curved part to the spatial distribution of pedestrians. Results for the headway distribution indicate that the curvature induces a more homogeneous distribution of pedestrians than the one observed for the straight part. The distribution on the straight part is more heterogeneous which seems to allow a more efficient use of the available space leading to larger flows.