Czechoslovak Mathematical Journal, Vol. 53, No. 4, pp. 1017-1030, 2003

# Contact elements on fibered manifolds

## 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

Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).