Contact elements on fibered manifolds. (English) Zbl 1080.58002

Kolář, Ivan; Mikulski, Włodyimierz M.

Czech. Math. J. 53, No. 4, 1017-1030 (2003).

Summary: 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 \(K_{k,l}^{r,s,q} Y\).

MSC:

58A20	Jets in global analysis
53A55	Differential invariants (local theory), geometric objects

Keywords:

jet of fibered manifold morphism; contact element; Weil bundle; natural operator

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