Geodesic
The natural affinors on some fiber product preserving gauge bundle functors of vector bundles
Archivum mathematicum, Tome 42 (2006) no. 1, pp. 59-67 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We classify all natural affinors on vertical fiber product preserving gauge bundle functors $F$ on vector bundles. We explain this result for some more known such $F$. We present some applications. We remark a similar classification of all natural affinors on the gauge bundle functor $F^*$ dual to $F$ as above. We study also a similar problem for some (not all) not vertical fiber product preserving gauge bundle functors on vector bundles.
We classify all natural affinors on vertical fiber product preserving gauge bundle functors $F$ on vector bundles. We explain this result for some more known such $F$. We present some applications. We remark a similar classification of all natural affinors on the gauge bundle functor $F^*$ dual to $F$ as above. We study also a similar problem for some (not all) not vertical fiber product preserving gauge bundle functors on vector bundles.
Classification : 58A20, 58A32
Keywords: gauge bundle functors; natural operators; natural transformations; natural affinors; jets 
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     title = {The natural affinors on some fiber product preserving gauge bundle functors of vector bundles},
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Kurek, Jan; Mikulski, Włodzimierz M. The natural affinors on some fiber product preserving gauge bundle functors of vector bundles. Archivum mathematicum, Tome 42 (2006) no. 1, pp. 59-67. http://geodesic.mathdoc.fr/item/ARM_2006_42_1_a6/

[1] Doupovec, M., Kolář, I.: Natural affinors on time-dependent Weil bundles. Arch. Math. (Brno) 27 (1991), 205–209. | MR

[2] Gancarzewicz, J., Kolář, I.: Natural affinors on the extended $r$-th order tangent bundles. Rend. Circ. Mat. Palermo (2) Suppl. 30 (1993), 95–100. | MR

[3] Kolář, I. et al.: Natural operations in differential geometry. Springer-Verlag, Berlin 1993. | MR

[4] Kolář, I., Mikulski, W. M.: Contact elements on fibered manifolds. Czechoslovak Math. J. 53(128) (2003), 1017–1030. | MR

[5] Kolář, I., Modugno M.: Torsions of connections on some natural bundles. Differential Geom. Appl. 2 (1992), 1–16. | MR

[6] Kurek, J.: Natural affinors on higher order cotangent bundles. Arch. Math. (Brno) 28 (1992), 175–180. | MR

[7] Kurek, J., Mikulski, W. M.: Some natural operators in linear vector fields. Ann. Univ. Mariae Curie-Skłodowska Sect. A 58 (2004), 87–95. | MR

[8] Mikulski, W. M.: On the fiber product preserving gauge bundle functors on vector bundles. Ann. Polon. Math. 82.3 (2003), 251–264. | MR | Zbl

[9] Mikulski, W. M.: Natural affinors on $r$-jet prolongation of the tangent bundles. Arch. Math. (Brno) 34(2) (1998), 321–328. | MR

[10] Mikulski, W. M.: Natural affinors on $(J^rT^*)^*$. Arch. Math. (Brno) 36 (2000), 261–267. | MR | Zbl

[11] Mikulski, W. M.: The natural affinors on $\otimes ^kT^{(r)}$. Note Mat. 19(2) (1999), 269–274. | MR

[12] Mikulski, W. M.: The natural affinors on generalized higher order tangent bundles. Rend. Mat. Appl. (7) 21 (2001), 339–349. | MR | Zbl

[13] Mikulski, W. M.: Natural affinors on $(J^{r,s,q}(\cdot ,\mathbf{R}^{1,1})_0)^*$. Comment. Math. Univ. Carolin. 42(4) (2001), 655–663. | MR | Zbl

[14] Mikulski, W. M.: The natural affinors on $(J^rT^{*,a})^*$. Acta Univ. Palack. Olomuc. Fac. Rerum Natur., Math. 40 (2001), 179–184. | MR | Zbl

[15] Mikulski, W. M.: The natural affinors on the $r$-jet prolongations of a vector bundle. Demonstratio Math. XXXVII (3) (2004), 709–717. | MR | Zbl

[16] Tomáš, J.: Natural operators transforming projectable vector fields to product preserving bundles. Rend. Circ. Mat. Palermo (2) Suppl. 59 (1999), 181–187. | MR