Geodesic
Lifting of projectable vector fields to vertical fiber product preserving vector bundles
Archivum mathematicum, Tome 42 (2006) no. 3, pp. 265-271 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We classify all natural operators lifting projectable vector fields from fibered manifolds to vector fields on vertical fiber product preserving vector bundles. We explain this result for some more known such bundles.
We classify all natural operators lifting projectable vector fields from fibered manifolds to vector fields on vertical fiber product preserving vector bundles. We explain this result for some more known such bundles.
Classification : 58A20, 58A32
Keywords: fibered manifolds; vector bundle functors; natural operators; natural transformations 
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     title = {Lifting of projectable vector fields to vertical fiber product preserving vector bundles},
     journal = {Archivum mathematicum},
     pages = {265--271},
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     zbl = {1164.58303},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2006_42_3_a8/}
}
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Mikulski, Włodzimierz M. Lifting of projectable vector fields to vertical fiber product preserving vector bundles. Archivum mathematicum, Tome 42 (2006) no. 3, pp. 265-271. http://geodesic.mathdoc.fr/item/ARM_2006_42_3_a8/

[1] Doupovec, M.: Natural operators transforming vector fields to the second order tangent bundle. Časopis pěst. mat. 115 (1990), 64–72. | MR | Zbl

[2] Kolář, I.: On the natural operators transforming vector fields to the $r$-th tensor power. Suppl. Rend. Math. Circ. Palermo II(32) (1993), 15–20. | MR

[3] Kolář, I., Michor, P. W., Slovák, J.: Natural operations in differential geometry. Springer-Verlag, Berlin 1993. | MR

[4] Kolář, I., Mikulski, W. M.: On the fiber product preserving bundle functors. Differential Geom. Appl. 11 (1999), 105–115.. | MR

[5] Kurek, J., Mikulski, W. M.: Lifting of linear vector fields to fiber product preserving vertical gauge bundles. Colloq. Math. 103(1) (2005), 33–40. | MR

[6] Mikulski, W. M.,: Some natural constructions on vector fields and higher order cotangent bundles. Monatsh. Math. 117 (1994), 107–115. | MR | Zbl

[7] Mikulski, W. M.,: Some natural operations on vector fields. Rend. Mat. Roma 12 (1992), 783–803. | MR | Zbl

[8] Mikulski, W. M.: The natural operators lifting projectable vector fields to some fiber product preserving bundles. Ann. Polon. Math. 81.3 (2003), 261–271. | MR | Zbl