imposing integrability conditions on a particular "g"-structure (for instance, with the case of a symplectic form) can be dealt with via the process of prolongation. in such cases, the prolonged "g"-structure cannot be identified with a "g"-subbundle of the bundle of linear frames. in many cases, however, the prolongation is a principal bundle in its own right, and its structure group can be identified with a subgroup of a higher-order jet group. in which case, it is called a higher order "g"-structure [kobayashi]. in general, cartan's equivalence method applies to such cases.