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Natural liftings of foliations to the \(r\)-tangent bundle. (English) Zbl 0848.57025
Bureš, J. (ed.) et al., Proceedings of the winter school on geometry and physics, Zdíkov, Czech Republic, January 1993. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 37, 153-159 (1994).
Let \(F\) be a \(p\)-dimensional foliation on an \(n\)-manifold \(M\), and \(T^r M\) the \(r\)-tangent bundle of \(M\). The purpose of this paper is to present some reltionship between the foliation \(F\) and a natural lifting of \(F\) to the bundle \(T^r M\). Let \(L^r_q (F)\) \((q=0, 1, \dots, r)\) be a foliation on \(T^r M\) projectable onto \(F\) and \(L^r_q= \{L^r_q (F)\}\) a natural lifting of foliations to \(T^r M\). The author proves the following theorem: Any natural lifting of foliations to the \(r\)-tangent bundle is equal to one of the liftings \(L^r_0, L^r_1, \dots, L^r_n\).
The exposition is clear and well organized.
For the entire collection see [Zbl 0823.00015].
57R30 Foliations in differential topology; geometric theory
53C12 Foliations (differential geometric aspects)
53C10 \(G\)-structures