# Article

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Keywords:
gauge bundle functors; natural operators; natural transformations; natural affinors; jets
Summary:
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.
References:
[1] Doupovec, M., Kolář, I.: Natural affinors on time-dependent Weil bundles. Arch. Math. (Brno) 27 (1991), 205–209. MR 1189217
[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 1246623
[3] Kolář, I. et al.: Natural operations in differential geometry. Springer-Verlag, Berlin 1993. MR 1202431
[4] Kolář, I., Mikulski, W. M.: Contact elements on fibered manifolds. Czechoslovak Math. J. 53(128) (2003), 1017–1030. MR 2018847
[5] Kolář, I., Modugno M.: Torsions of connections on some natural bundles. Differential Geom. Appl. 2 (1992), 1–16. MR 1244453
[6] Kurek, J.: Natural affinors on higher order cotangent bundles. Arch. Math. (Brno) 28 (1992), 175–180. MR 1222284
[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 2199593
[8] Mikulski, W. M.: On the fiber product preserving gauge bundle functors on vector bundles. Ann. Polon. Math. 82.3 (2003), 251–264. MR 2040810 | Zbl 1126.58300
[9] Mikulski, W. M.: Natural affinors on $r$-jet prolongation of the tangent bundles. Arch. Math. (Brno) 34(2) (1998), 321–328. MR 1645340
[10] Mikulski, W. M.: Natural affinors on $(J^rT^*)^*$. Arch. Math. (Brno) 36 (2000), 261–267. MR 1811170 | Zbl 1090.58501
[11] Mikulski, W. M.: The natural affinors on $\otimes ^kT^{(r)}$. Note Mat. 19(2) (1999), 269–274. MR 1816880
[12] Mikulski, W. M.: The natural affinors on generalized higher order tangent bundles. Rend. Mat. Appl. (7) 21 (2001), 339–349. MR 1884952 | Zbl 1048.58004
[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 1883375 | Zbl 1050.58004
[14] Mikulski, W. M.: The natural affinors on $(J^rT^{*,a})^*$. Acta Univ. Palack. Olomuc. Fac. Rerum Natur., Math. 40 (2001), 179–184. MR 1904693 | Zbl 1050.58004
[15] Mikulski, W. M.: The natural affinors on the $r$-jet prolongations of a vector bundle. Demonstratio Math. XXXVII (3) (2004), 709–717. MR 2093550 | Zbl 1064.58003
[16] Tomáš, J.: Natural operators transforming projectable vector fields to product preserving bundles. Rend. Circ. Mat. Palermo (2) Suppl. 59 (1999), 181–187. MR 1692269

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