Muñoz Masqué, JaimeValdés Morales, Antonio2023-06-202023-06-2019971120-7183https://hdl.handle.net/20.500.14352/58669Let M be an n -dimensional manifold, π: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 π ¯ :F(M)/G→M . A functorial connection is an assignment of a linear connection ∇(σ) on M to each section σ of the bundle π ¯ which satisfies the following properties: ∇(σ) is reducible to the subbundle P σ ⊂FM corresponding to σ , depends continuously on σ , and for every diffeomorphism f:M→M there holds ∇(f⋅σ)=f⋅∇(σ) . 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.journal articlehttp://www1.mat.uniroma1.it/ricerca/rendiconti/http://www.mat.uniroma1.it/people/rendiconmetadata only access514.7Differential systemsjet bundleslinear representationsG-structuresfunctorial connectionsgeometric differential invariantsGeometría diferencial1204.04 Geometría Diferencial