Topic summary
Method of moving frames
Extracted from the Wikipedia article Moving frame.
Further details
The method of moving frames of Élie Cartan is based on taking a moving frame that is adapted to the particular problem being studied. For example, given a curve in space, the first three derivative vectors of the curve can in general define a frame at a point of it (cf. torsion tensor for a quantitative description – it is assumed here that the torsion is not zero). In fact, in the method of moving frames, one more often works with coframes rather than frames. More generally, moving frames may be viewed as sections of principal bundles over open sets U. The general Cartan method exploits this abstraction using the notion of a Cartan connection.