Bonnet did important work on differential geometry, a topic that was also being investigated in France by Serret, Frenet, Bertrand and Puiseux. Here Bonnet made major contributions to the concept of curvature. In particular, he published a formula relating the surface integral of the Gauss curvature to the Euler characteristic of the surface and the line integral of the geodesic curvature of its boundary; this result is now known as the Gauss–Bonnet theorem. Gauss was known to have previously discovered a special case of this fundamental result, but had never published it.