Structure tensor of a field of geometric objects (Q1107125)

A construction of a kth structure tensor of a field of geometric objects is presented. For a given field \(\sigma\) the author constructs a vector bundle \(H^{k,2}(\sigma)\). The kth structure tensor is defined as a section of \(H^{k,2}(\sigma)\) generated by the torsion of \(\sigma\). It is then shown that the vanishing of the kth structure tensor is a necessary and sufficient condition for the field to be \((k+1)\)-flat.