Editing G-structure on a manifold (section)

== Higher order ''G''-structures ==

Imposing [[integrability condition]]s on a particular ''G''-structure (for instance, with the case of a symplectic form) can be dealt with via the process of [[Cartan's equivalence method|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.