RT Journal Article
T1 A report on functorial connections and differential invariants
A1 Muñoz Masqué, Jaime
A1 Valdés Morales, Antonio
AB 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.
PB Università degli Studi di Roma "La Sapienza". Dipartamento di Matematica
SN 1120-7183
YR 1997
FD 1997
LK https://hdl.handle.net/20.500.14352/58669
UL https://hdl.handle.net/20.500.14352/58669
DS Docta Complutense
RD 11 abr 2025