  We find three characterizations for a multidimensional (n+1)-web W possessing
a reduct reducible subweb: its closed form equations, the integrability of an
invariant distribution associated with W, and the relations between the
components of its torsion tensor. In the case of codimension one, the latter
criterion establishes a relation with solutions of a system of nonlinear
second-order PDEs. Some particular cases of this system were considered by
Goursat in 1899.
