The natural affinors on some fiber product preserving gauge bundle functors of vector bundles

Jan Kurek; Włodzimierz M. Mikulski

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 1, page 59-67
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Kurek, Jan, and Mikulski, Włodzimierz M.. "The natural affinors on some fiber product preserving gauge bundle functors of vector bundles." Archivum Mathematicum 042.1 (2006): 59-67. <http://eudml.org/doc/249830>.

@article{Kurek2006,
abstract = {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.},
author = {Kurek, Jan, Mikulski, Włodzimierz M.},
journal = {Archivum Mathematicum},
keywords = {gauge bundle functors; natural operators; natural transformations; natural affinors; jets; natural operators; natural transformations; natural affinors; jets},
language = {eng},
number = {1},
pages = {59-67},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The natural affinors on some fiber product preserving gauge bundle functors of vector bundles},
url = {http://eudml.org/doc/249830},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Kurek, Jan
AU - Mikulski, Włodzimierz M.
TI - The natural affinors on some fiber product preserving gauge bundle functors of vector bundles
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 1
SP - 59
EP - 67
AB - 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.
LA - eng
KW - gauge bundle functors; natural operators; natural transformations; natural affinors; jets; natural operators; natural transformations; natural affinors; jets
UR - http://eudml.org/doc/249830
ER -

References

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  1. Natural affinors on time-dependent Weil bundles, Arch. Math. (Brno) 27 (1991), 205–209. MR1189217
  2. Natural affinors on the extended r -th order tangent bundles, Rend. Circ. Mat. Palermo (2) Suppl. 30 (1993), 95–100. MR1246623
  3. Natural operations in differential geometry, Springer-Verlag, Berlin 1993. MR1202431
  4. Contact elements on fibered manifolds, Czechoslovak Math. J. 53(128) (2003), 1017–1030. MR2018847
  5. Torsions of connections on some natural bundles, Differential Geom. Appl. 2 (1992), 1–16. MR1244453
  6. Natural affinors on higher order cotangent bundles, Arch. Math. (Brno) 28 (1992), 175–180. MR1222284
  7. Some natural operators in linear vector fields, Ann. Univ. Mariae Curie-Skłodowska Sect. A 58 (2004), 87–95. MR2199593
  8. On the fiber product preserving gauge bundle functors on vector bundles, Ann. Polon. Math. 82.3 (2003), 251–264. Zbl1126.58300MR2040810
  9. Natural affinors on r -jet prolongation of the tangent bundles, Arch. Math. (Brno) 34(2) (1998), 321–328. MR1645340
  10. Natural affinors on ( J r T * ) * , Arch. Math. (Brno) 36 (2000), 261–267. Zbl1090.58501MR1811170
  11. The natural affinors on ⊗ k T ( r ) , Note Mat. 19(2) (1999), 269–274. MR1816880
  12. The natural affinors on generalized higher order tangent bundles, Rend. Mat. Appl. (7) 21 (2001), 339–349. Zbl1048.58004MR1884952
  13. Natural affinors on ( J r , s , q ( · , 𝐑 1 , 1 ) 0 ) * , Comment. Math. Univ. Carolin. 42(4) (2001), 655–663. Zbl1050.58004MR1883375
  14. The natural affinors on ( J r T * , a ) * , Acta Univ. Palack. Olomuc. Fac. Rerum Natur., Math. 40 (2001), 179–184. Zbl1050.58004MR1904693
  15. The natural affinors on the r -jet prolongations of a vector bundle, Demonstratio Math. XXXVII (3) (2004), 709–717. Zbl1064.58003MR2093550
  16. Natural operators transforming projectable vector fields to product preserving bundles, Rend. Circ. Mat. Palermo (2) Suppl. 59 (1999), 181–187. MR1692269

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