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

Autores: Wlodzimierz M. Mikulski
Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 21, Nº 3, 2006, págs. 273-286
Idioma: inglés
Títulos paralelos:
- Prolongación de formas valuadas tangentes semibásicas lineales a haces gauge de haces vectoriales que conservan el producto
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Resumen
- Let A be a Weil algebra and V be an A-module with dimR V < 8. 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,Vf : TA,V E ? ?pT*TAM ÄTAM TTA,VE on TA,VE ? TAM from a linear semibasic tangent valued p-form f : E ? ?pT*M Ä TE on E ? M. For the Frolicher-Nijenhuis bracket we prove that [[TA,Vf, TA,V?]] = TA,V ([[f,?]]) for any linear semibasic tangent valued p- and q-forms f and ? on E ? M. We apply these results to linear general connections on E ? M.