Contact Elements on Fibered Manifolds

Abstract

For every product preserving bundle functor T ^μ on fibered manifolds, we describe the underlying functor of any order (r, s, q), s ≥ r ≤ 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 μ. We also determine all natural transformations of $K_{k,l}^{r,s,q} Y$ into itself and of $T\left( {K_{k,l}^{r,s,q} Y} \right)$ into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from Y to $K_{k,l}^{r,s,q} Y$.