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oai:docta.ucm.es:20.500.14352/586692023-08-28T06:25:51Zcom_20.500.14352_14col_20.500.14352_15

A report on functorial connections and differential invariants Muñoz Masqué, Jaime Valdés Morales, Antonio 514.7 Differential systems jet bundles linear representations G-structures functorial connections geometric differential invariants Geometría diferencial 1204.04 Geometría Diferencial Let 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. Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T18:48:19Z 2023-06-20T18:48:19Z 1997 journal article https://hdl.handle.net/20.500.14352/58669 1120-7183 metadata only access Università degli Studi di Roma "La Sapienza". Dipartamento di Matematica