G-Man (slang) G-Man (slang) G-Man (short for "Government Man") is an American slang term for special agents of the United States Government. It is specifically used as a term for a Federal Bureau of Investigation (FBI) agent. "G-Man" is also a term used for members of G Division, essentially a British anti-rebel police unit operating out of Dublin Castle prior to Irish Independence in 1922. Colonel Ned Broy uses the term in his official testimony for the Irish Army's Bureau of Military History in their archive of the Easter Rising (1916) and the Irish War of Independence (1919-1921). According to the "Merriam-Webster
G-structure on a manifold Frobenius theorem applies. A flat "G"-structure is a "G"-structure "P" having a global section ("V"...,"V") consisting of commuting vector fields. A "G"-structure is integrable (or "locally flat") if it is locally isomorphic to a flat "G"-structure. The set of diffeomorphisms of "M" that preserve a "G"-structure is called the "automorphism group" of that structure. For an O("n")-structure they are the group of isometries of the Riemannian metric and for an SL("n",R)-structure volume preserving maps. 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