G-Man (Half-Life) refers to simply as his "employers". His mysterious nature has made him an icon of the "Half-Life" series, with his identity and motives remaining almost completely unexplained. The G-Man's name comes from "G-Man", an American colloquialism meaning "Government Man". However, within the "Half-Life" games, he is identified by this name only in the program code and the multiplayer profile menu as a default name option, not within the story itself; his name is derived from his "Half-Life" model and entity name and has since been reused in subsequent games of the series. His name has been confirmed and he has
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