Contact elements on fibered manifolds

Kolář, Ivan ; Mikulski, Włodzimierz M.

Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 1017-1030

Résumé

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 $K_{k,l}^{r,s,q} Y$.

Détail

Classification : 53A55, 58A20
Keywords: jet of fibered manifold morphism; contact element; Weil bundle; natural operator