Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.

Mikulski, Wlodzimierz M.. "Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.." Extracta Mathematicae 21.3 (2006): 273-286. <http://eudml.org/doc/41865>.

@article{Mikulski2006,
abstract = {Let A be a Weil algebra and V be an A-module with dimR V &lt; ∞. 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.},
author = {Mikulski, Wlodzimierz M.},
journal = {Extracta Mathematicae},
keywords = {Variedades diferenciables; Haces vectoriales; Functores; linear semibasic tangent valued form; Weil algebra; gauge bundle functor; Frolicher-Nijenhuis bracket; generalized Weil bundle; canonical affinor},
language = {eng},
number = {3},
pages = {273-286},
title = {Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.},
url = {http://eudml.org/doc/41865},
volume = {21},
year = {2006},
}

TY - JOUR
AU - Mikulski, Wlodzimierz M.
TI - Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.
JO - Extracta Mathematicae
PY - 2006
VL - 21
IS - 3
SP - 273
EP - 286
AB - Let A be a Weil algebra and V be an A-module with dimR V &lt; ∞. 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.
LA - eng
KW - Variedades diferenciables; Haces vectoriales; Functores; linear semibasic tangent valued form; Weil algebra; gauge bundle functor; Frolicher-Nijenhuis bracket; generalized Weil bundle; canonical affinor
UR - http://eudml.org/doc/41865
ER -