Geodesic
On the flow prolongation of vector fields
Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 24 (2003), pp. 69-80
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Let $F$ be a fiber product preserving bundle functor of the base order $r$ on the category $\mathcal{FM}_m$ and $\eta$ a projectable vector field on $Y\to M$ over a vector field $\xi$ on $M,m=\dim M$. We construct a natural map transforming $F\eta$ and $j^r\xi$ into the flow prolongation of $\eta$ and deduce its basic properties. Our main tool is a similar construction in the case of products of two manifolds and of product vector fields. 
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     author = {I. Kolar},
     title = {On the flow prolongation of vector fields},
     journal = {Trudy Geometricheskogo Seminara},
     pages = {69--80},
     year = {2003},
     volume = {24},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/KUTGS_2003_24_a7/}
}
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I. Kolar. On the flow prolongation of vector fields. Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 24 (2003), pp. 69-80. http://geodesic.mathdoc.fr/item/KUTGS_2003_24_a7/