Singularities in the geometry of an obstacle
Given a fibered manifold , a 2-connection on means a section . The authors determine all first order natural operators transforming a 2-connection on and a classical linear connection on into a connection on . (The proof implies that there is no first order natural operator transforming 2-connections on into connections on .) Using this result, the authors deduce several properties of characterizable connections on .
For a three-web of codimension on a differentiable manifold of dimension , the author studies the Chern connection and a family of parallelizing connections. The latter ones have a common property with the former: the web-distributions are parallel with respect to them.