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A report on functorial connections and differential invariants

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Muñoz Masqué, Jaime and Valdés Morales, Antonio (1997) A report on functorial connections and differential invariants. Rendiconti di Matematica e delle sue Applicazioni. Serie VII , 17 (3). pp. 549-567. ISSN 1120-7183

Official URL: http://www1.mat.uniroma1.it/ricerca/rendiconti/




Abstract

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.


Item Type:Article
Uncontrolled Keywords:Differential systems; jet bundles; linear representations; G-structures; functorial connections; geometric differential invariants
Subjects:Sciences > Mathematics > Differential geometry
ID Code:22451
Deposited On:19 Jul 2013 07:43
Last Modified:12 Dec 2018 15:13

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