Let $G$ be a bundle functor of order $(r,s,q)$, $s\ge r\le q$, on the category $ℱ{ℳ}_{m,n}$ of $(m,n)$-dimensional fibered manifolds and local fibered diffeomorphisms. Given a general connection $\Gamma$ on an $ℱ{ℳ}_{m,n}$-object $Y\to M$ we construct a general connection $𝒢(\Gamma ,\lambda ,\Lambda )$ on $GY\to Y$ be means of an auxiliary $q$-th order linear connection $\lambda$ on $M$ and an $s$-th order linear connection $\Lambda$ on $Y$. Then we construct a general connection $𝒢(\Gamma ,{\nabla }_1,{\nabla }_2)$ on $GY\to Y$ by means of auxiliary classical linear connections ${\nabla }_1$ on $M$ and ${\nabla }_2$ on $Y$. In the case $G=J^1$ we determine all general connections $𝒟(\Gamma ,\nabla )$ on $J^{1}Y\to Y$ from...

This paper contains a classification of all affine liftings of torsion-free linear connections on n-dimensional manifolds to any linear connections on Weil bundles under the condition that n ≥ 3.

Weil algebra morphisms induce natural transformations between Weil bundles. In some well known cases, a natural transformation is endowed with a canonical structure of affine bundle. We show that this structure arises only when the Weil algebra morphism is surjective and its kernel has null square. Moreover, in some cases, this structure of affine bundle passes to jet spaces. We give a characterization of this fact in algebraic terms. This algebraic condition also determines an affine structure...