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Title: Natural liftings of foliations to the $r$-tangent bunde (English)
Author: Mikulski, Włodzimierz M.
Language: English
Journal: Proceedings of the Winter School "Geometry and Physics"
Issue: 1993
Pages: [153]-159
Category: math
Summary: 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 $L^r_0, L^r_1, \dots, L^r_n$. \par The exposition is clear and well organized. (English)
MSC: 53A55
MSC: 53C10
MSC: 53C12
MSC: 57R30
MSC: 58A20
idZBL: Zbl 0848.57025
idMR: MR1344008
Date available: 2009-07-13T21:33:32Z
Last updated: 2012-09-18
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