Abstract
First introduced by Gaston Darboux, and then brought to maturity by Ehe Cartan, [4, 5], the theory of moving frames (“repères mobiles”) is widely acknowledged to be a powerful tool for studying the geometric properties of submanifolds under the action of a transformation group. While the basic ideas of moving frames for classical group actions are now ubiquitous in differential geometry, the theory and practice of the moving frame method for more general transformation group actions has remained relatively undeveloped. The famous critical assessment by Weyl in his review [27] of Cartan’s seminal book [5] retains its perspicuity to this day:
I did not quite understand how he [Cartan] does this in general, though in the examples he gives the procedure is clear Nevertheless, I must admit I found the book, like most of Cartan’s papers, hard reading.
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Fels, M., Olver, P.J. (2001). Moving Frames and Coframes. In: Saint-Aubin, Y., Vinet, L. (eds) Algebraic Methods in Physics. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0119-6_4
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