Some applications of the Mangiarotti-Modugno formula for tangent-valued forms (Q2925091)

The author presents a classical approach to a general connection on an arbitrary fibered manifold \(Y\to M\). He presents the covariant approach to the Weil bundle for every Weil algebra \(A\), that generalizes the concept of \((k,r)\)-velocity introduced by Ehresmann. He introduces the concept of a-torsion of an arbitrary tangent-valued form on a Weil bundle \(T^{A}M\), for any \(a\in A\). Applying the graded Jacobi identity, he proves a far-going generalization of a first Bianchi identity for classical connections in terms of a Frölicher-Nijenhuis bracket and he deduces two results concerning \(f\)-relatedness, for a differentiable map \(f:M\to N\), which clarifies a remarkable functorial character of a-torsion.