From the point of view of the differential geometry of fiber bundles, the n vector fields { e a } a = 1 … … n define a section of the frame bundle i.e. a parallelization of U ⊂ ⊂ M which is equivalent to an isomorphism T U ≅ ≅ U × × R n . Since not every manifold is parallelizable, a vielbein can generally only be chosen locally (i.e. only on a coordinate chart U and not all of M .)