Natural liftings of foliations to the $r$-tangent bunde

Natural liftings of foliations to the

r

-tangent bunde

Mikulski, Włodzimierz M.

Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1994), p. [153]-159 / Harvested from

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Résumé

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 $L_{q}^{r} (F)$ $(q = 0, 1, \dots, r)$ be a foliation on $T^{r} M$ projectable onto $F$ and $L_{q}^{r} = {L_{q}^{r} (F)}$ 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 $L_{0}^{r}, L_{1}^{r}, \dots, L_{n}^{r}$ . The exposition is clear and well organized.

MR MR1344008 | Zbl 0848.57025

EUDML-ID : urn:eudml:doc:220901
Mots clés:

@article{701552,
     title = {Natural liftings of foliations to the $r$-tangent bunde},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1994},
     pages = {[153]-159},
     mrnumber = {MR1344008},
     zbl = {0848.57025},
     url = {http://dml.mathdoc.fr/item/701552}
}

Mikulski, Włodzimierz M. Natural liftings of foliations to the $r$-tangent bunde, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1994), pp. [153]-159. http://gdmltest.u-ga.fr/item/701552/