Geodesic
Canonical 1-forms on higher order adapted frame bundles
Archivum mathematicum, Tome 44 (2008) no. 2, pp. 115-118

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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 $\mathbf{R}$. We describe all canonical (${\mathcal{F}}\mbox {\it ol}_{m,n}$-invariant) $V$-valued $1$-forms $\Theta \colon TP^r(M,{\mathcal{F}}) \rightarrow V$ on the $r$-th order adapted frame bundle $P^r(M,\mathcal{F})$ of $(M,\mathcal{F})$.
Classification : 58A20, 58A32
Keywords: foliated manifold; infinitesimal automorphism; higher order adapted frame bundle; canonical $1$-form 
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     author = {Kurek, Jan and Mikulski, W{\l}odzimierz M.},
     title = {Canonical 1-forms on higher order adapted frame bundles},
     journal = {Archivum mathematicum},
     pages = {115--118},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2008},
     mrnumber = {2432848},
     zbl = {1212.58002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2008__44_2_a3/}
}
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Kurek, Jan; Mikulski, Włodzimierz M. Canonical 1-forms on higher order adapted frame bundles. Archivum mathematicum, Tome 44 (2008) no. 2, pp. 115-118. http://geodesic.mathdoc.fr/item/ARM_2008__44_2_a3/