Cartan formalism
This article should be merged with vierbein.Elie Cartan reformulated the differential geometry of(pseudo) Riemannian geometry (and not just metric manifolds, but any arbitrary manifold, including Lie group manifolds) in terms of "moving frames" (repère mobile) as an alternative reformulation of general relativity.
In differential geometry, Cartan formalism is an alternative approach to covariant derivatives and curvature, using differential forms and frames. Although it is frame dependent, it is very well suited for computations. It can also be understood in terms of frame bundles, and it allows generalizations like the spinor bundle, and also the principal bundle.
The main idea is to develop expressions for connectionss and curvature using orthogonal frames.
