Canonical \(1\)-forms on higher order adapted frame bundles. (English) Zbl 1212.58002

Kurek, Jan; Mikulski, Włodzimierz M.

Arch. Math., Brno 44, No. 2, 115-118 (2008).

Summary: Let \((M,\mathcal F)\) be a foliated \((m+n)\)-dimensional manifold \(M\) with \(n\)-dimensional foliation \(\mathcal F\). Let \(V\) be a finite dimensional vector space over \(\mathbb R\). We describe all canonical (\({\mathcal F}ol_{m,n}\)-invariant) \(V\)-valued \(1\)-forms \(\Theta \: TP^r(M,{\mathcal F}) \to V\) on the \(r\)-th order adapted frame bundle \(P^r(M,\mathcal F)\) of \((M,\mathcal F)\).

MSC:

58A20	Jets in global analysis
58A32	Natural bundles

Keywords:

foliated manifold; infinitesimal automorphism; higher order adapted frame bundle, canonical \(1\)-form