The Exterior Derivation and the Orders of Differential Forms on Contractible Algebras.
For natural numbers n ≥ 3 and r a complete description of all natural bilinear operators is presented. Next for natural numbers r and n ≥ 3 a full classification of all natural linear operators is obtained.
The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form itself is closely related to the shape map of the connection. The codimension one case generalises the traditional shape operator of Riemannian geometry.