Higher order reduction theorems for classical connections and natural   (0,2)-tensor fields on the cotangent bundle
  We generalize reduction theorems for classical connections to operators with values in $k$-th order natural bundles. Using the first reduction theorem in order two we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection. 
Josef Jany\v{s}ka