## W.M. Mikulski

*A construction of a connection on $GY\to Y$ from a connection on $Y\to M$ by means of classical linear connections on $M$ and $Y$ *

Comment.Math.Univ.Carolinae 46,4 (2005) 759-770. **Abstract:**Let $G$ be a bundle functor of order $(r,s,q)$, $s\geq r\leq q$, on the category $\Cal F\Cal M_{m,n}$ of $(m,n)$-dimensional fibered manifolds and local fibered diffeomorphisms. Given a general connection $\Gamma $ on an $\Cal F\Cal M_{m,n}$-object $Y\to M$ we construct a general connection $\Cal G(\Gamma ,\lambda ,\Lambda )$ 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 $\Cal G (\Gamma ,\nabla _1,\nabla _2)$ 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 $\Cal D(\Gamma ,\nabla )$ on $J^1Y\to Y$ from general connections $\Gamma $ on $Y\to M$ by means of torsion free projectable classical linear connections $\nabla $ on $Y$.

**Keywords:** general connection, classical linear connection, bundle functor, natural operator

**AMS Subject Classification:** 58A05, 58A20, 58A32

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