Some applications of the Mangiarotti–Modugno formula for tangent-valued forms

Abstract

First, we present a classical approach to the general connections on arbitrary fibered manifolds. Then we compare this approach with the use of the Frölicher–Nijenhuis bracket by Mangiarotti and Modugno [Graded Lie algebras and connections on a fibered space, J. Math. Pures Appl. 63 (1984) 111–120]. Finally, we demonstrate that the latter viewpoint is very efficient in the theory of torsions of connections on Weil bundles.