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

Wlodzimierz M. Mikulski

Extracta Mathematicae (2006)

  • Volume: 21, Issue: 3, page 273-286
  • ISSN: 0213-8743

Abstract

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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.

How to cite

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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 -

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