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

Wlodzimierz M. Mikulski

• 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.