Abstract
A study is made of the rings A r of r-order differential invariants of linear frames on a differentiable manifold X with respect to the Lie algebra of the vector fields of X. It is demostrated that, locally, such rings are differentiably finitely generated and canonical bases are determined. The global structure of the rings A r and that of the subrings A′ r ⊆ A r of differential invariants under the group of the diffeomorphisms of X are determined. As an application of the theory the problem of local equivalence of complete parallelisms is solved, demonstrating that the equality of the basic differential invariants of two fields of linear frames are sufficient conditions for their formal equivalence (and hence, analytical).
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