Geodesic
Connections of higher order and product preserving functors
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 4, pp. 889-896 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we consider a product preserving functor $\mathcal F$ of order $r$ and a connection $\Gamma $ of order $r$ on a manifold $M$. We introduce horizontal lifts of tensor fields and linear connections from $M$ to $\mathcal F(M)$ with respect to $\Gamma $. Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.
In this paper we consider a product preserving functor $\mathcal F$ of order $r$ and a connection $\Gamma $ of order $r$ on a manifold $M$. We introduce horizontal lifts of tensor fields and linear connections from $M$ to $\mathcal F(M)$ with respect to $\Gamma $. Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.
Classification : 53C05, 58A20, 58A32
Keywords: connections of higher order; product preserving functors; lifts of tensors and connections 
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     author = {Gancarzewicz, Jacek and Rahmani, Noureddine and Salgado, Modesto},
     title = {Connections of higher order and product preserving functors},
     journal = {Czechoslovak Mathematical Journal},
     pages = {889--896},
     year = {2002},
     volume = {52},
     number = {4},
     mrnumber = {1940068},
     zbl = {1020.53012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_4_a19/}
}
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Gancarzewicz, Jacek; Rahmani, Noureddine; Salgado, Modesto. Connections of higher order and product preserving functors. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 4, pp. 889-896. http://geodesic.mathdoc.fr/item/CMJ_2002_52_4_a19/