Talk:G-structure

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[edit] Integrability condition versus other conditions

Although I stated that integrability conditions were the primary reason for higher-order G-structures, this really isn't the case at all. It is only the easiest way to see it. For example, a conformal structure induces a higher order G-structure because the associated prolongation of the principal bundle can be canonically embedded into the principal bundle of holonomic second-order frames. Gotta run right now, though. Silly rabbit 00:33, 15 November 2005 (UTC)

[edit] Chern

The article says that G-structures were introduced by Chern, but I can't find any evidence of this. Can anyone confirm? The 1966 article by Chern on G-structures references older papers by Cartan (1908 and 1953) and Bernard (1960). These appear to be in French, however, so I can't read them. -- Fropuff (talk) 17:09, 6 March 2008 (UTC)

It's fairly doubtful that Chern was responsible for introducing them. Do you have a full citation for the Cartan 1953 paper? (The 1908 paper predates the innovation of the fibre bundle, so should probably be disqualified.) Silly rabbit (talk) 17:19, 6 March 2008 (UTC)

The one Chern references is: E. Cartan (1953), Pseudo-groupes continus infinis. Geometrie differentielle, Colloquium, Strasbourg, pp. 119–136, Centre National de la Recherche Scientifique, Paris. -- Fropuff (talk) 17:25, 6 March 2008 (UTC)

G-structures were introduced and extensively studied by Cartan. See Part 2 and Part 3 of Cartan's "Oeuvres Completes" , Gauthier-Villars, 1955 Tiphareth (talk) 22:59, 7 March 2008 (UTC)