Invariant tensorfields and the canonical connection of a 3-web

In the following we shall give a new approach to web geometry. Instead of using the reduced adapted coframe bundles over the web manifolds we define invariant tensorfields corresponding to the 3-web structure and express the covariant derivation of the Chern connection with the help of these tensorfields, working only on the tangent bundle of the web manifold. The invariant tensorfields of a 3-web define a more general, so-called {H, J}-structure on the manifold which can be considered as an infinitesimal, non-integrable version of a web structure. We introduce a canonical connection of a {H, J}-structure which reduces to the Chern connection in the case of a 3-web. Using the tensorial expression of the covariant derivation of the Chern connection we give direct proof for the torsion and curvature identities. Finally, we apply our formulae to an algebraic characterization of the parallel translation with respect to the Chern connection.