Geodesic
Contact elements on fibered manifolds
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 1017-1030
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For every product preserving bundle functor $T^\mu $ on fibered manifolds, we describe the underlying functor of any order $(r,s,q), s\ge r\le q$. We define the bundle $K_{k,l}^{r,s,q} Y$ of $(k,l)$-dimensional contact elements of the order $(r,s,q)$ on a fibered manifold $Y$ and we characterize its elements geometrically. Then we study the bundle of general contact elements of type $\mu $. We also determine all natural transformations of $K_{k,l}^{r,s,q} Y$ into itself and of $T(K_{k,l}^{r,s,q} Y)$ into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from $Y$ to $K_{k,l}^{r,s,q} Y$.
For every product preserving bundle functor $T^\mu $ on fibered manifolds, we describe the underlying functor of any order $(r,s,q), s\ge r\le q$. We define the bundle $K_{k,l}^{r,s,q} Y$ of $(k,l)$-dimensional contact elements of the order $(r,s,q)$ on a fibered manifold $Y$ and we characterize its elements geometrically. Then we study the bundle of general contact elements of type $\mu $. We also determine all natural transformations of $K_{k,l}^{r,s,q} Y$ into itself and of $T(K_{k,l}^{r,s,q} Y)$ into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from $Y$ to $K_{k,l}^{r,s,q} Y$.
Classification : 53A55, 58A20
Keywords: jet of fibered manifold morphism; contact element; Weil bundle; natural operator 
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     author = {Kol\'a\v{r}, Ivan and Mikulski, W{\l}odzimierz M.},
     title = {Contact elements on fibered manifolds},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1017--1030},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2003_53_4_a18/}
}
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Kolář, Ivan; Mikulski, Włodzimierz M. Contact elements on fibered manifolds. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 1017-1030. http://geodesic.mathdoc.fr/item/CMJ_2003_53_4_a18/

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