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General covariant transformations


In physics, general covariant transformations are symmetries of gravitation theory on a world manifold . They are gauge transformations whose parameter functions are vector fields on . From the physical viewpoint, general covariant transformations are treated as particular (holonomic) reference frame transformations in general relativity. In mathematics, general covariant transformations are defined as particular automorphisms of so-called natural fiber bundles.

Let be a fibered manifold with local fibered coordinates . Every automorphism of is projected onto a diffeomorphism of its base . However, the converse is not true. A diffeomorphism of need not give rise to an automorphism of .


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