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Czechoslovak Mathematical Journal, Vol. 53, No. 4, pp. 1017-1030, 2003
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Contact elements on fibered manifolds

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Ivan Kolar, Wlodyimierz M. Mikulski

* I. Kolar*, Department of Algebra and Geometry, Masaryk University, Janackovo nam. 2a, 662 95 Brno, Czech Republic, e-mail: ` kolar@math.muni.cz`; * W. M. Mikulski*, Institute of Mathematics Jagellonian University, Reymonta 4, Krakow, Poland, e-mail: ` mikulski@im.uj.edu.pl`

**Abstract:** For every product preserving bundle functor $T^\mu$ on fibered manifolds, we describe the underlying functor of any order $(r,s,q), s\geq r\leq q$. 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 $K_{k,l}^{r,s,q} Y$.

**Keywords:** jet of fibered manifold morphism, contact element, Weil bundle, natural operator

**Classification (MSC 2000):** 58A20, 53A55

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