let "p" be a "g"-structure on a manifold "m", and "q" a "g"-structure on a manifold "n". then an isomorphism of the "g"-structures is a diffeomorphism "f" : "m" → "n" such that the pushforward of linear frames "f" : "fm" → "fn" restricts to give a mapping of "p" into "q". (note that it is sufficient that "q" be contained within the image of "f".) the "g"-structures "p" and "q" are locally isomorphic if "m" admits a covering by open sets "u" and a family of diffeomorphisms "f" : "u" → "f"("u") ⊂ "n" such that "f" induces an isomorphism of "p"| → "q"|.