Contact Elements on Fibered Manifolds

For every product preserving bundle functor Tμ on fibered manifolds, we describe the underlying functor of any order (r, s, q), s ≥ r ≤ q. We define the bundle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$K_{k,l}^{r,s,q} Y$$ \end{document} 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$K_{k,l}^{r,s,q} Y$$ \end{document} into itself and of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$T\left( {K_{k,l}^{r,s,q} Y} \right)$$ \end{document} into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from Y to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$K_{k,l}^{r,s,q} Y$$ \end{document}.