Resumen:
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Let M be an n -dimensional manifold, ?:F(M)?M the linear frame bundle, and G a closed subgroup of GL(n,R) . As is known, there is a one-to-one correspondence between the G -structures on M and the sections of the bundle ? ¯ :F(M)/G?M . A functorial connection is an assignment of a linear connection ?(?) on M to each section ? of the bundle ? ¯ which satisfies the following properties: ?(?) is reducible to the subbundle P ? ?FM corresponding to ? , depends continuously on ? , and for every diffeomorphism f:M?M there holds ?(f??)=f??(?) .
The article is a survey of the authors' recent results concerning functorial connections and their use in constructing differential invariants of G -structures. The most attention is concentrated on the problem of existence of a functorial connection for a given subgroup G?GL(n,R) and on the calculation of the number of functionally independent differential invariants of a given order. Special consideration is devoted to the G -structures determined by linear and projective parallelisms and by pseudo-Riemannian metrics.
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