Let A be a Weil algebra and V be an A-module with dimR V < ∞. Let E → M be a vector bundle and let TA,VE → TAM be the vector bundle corresponding to (A,V). We construct canonically a linear semibasic tangent valued p-form TA,Vφ : TA,V E → ΛpT*TAM ⊗TAM TTA,VE on TA,VE → TAM from a linear semibasic tangent valued p-form φ : E → ΛpT*M ⊗ TE on E → M. For the Frolicher-Nijenhuis bracket we prove that [[TA,Vφ, TA,Vψ]] = TA,V ([[φ,ψ]]) for any linear semibasic tangent valued p- and q-forms φ and ψ on E → M. We apply these results to linear general connections on E → M.
@article{urn:eudml:doc:41865,
title = {Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.},
journal = {Extracta Mathematicae},
volume = {21},
year = {2006},
pages = {273-286},
zbl = {1131.58002},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41865}
}
Mikulski, Wlodzimierz M. Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.. Extracta Mathematicae, Tome 21 (2006) pp. 273-286. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41865/