Prolongation of projectable tangent valued forms

Antonella Cabras; Ivan Kolář

Archivum Mathematicum (2002)

  • Volume: 038, Issue: 4, page 243-257
  • ISSN: 0044-8753

Abstract

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First we deduce some general properties of product preserving bundle functors on the category of fibered manifolds. Then we study the prolongation of projectable tangent valued forms with respect to these functors and describe the complete lift of the Frölicher-Nijenhuis bracket. We also present the coordinate formula for composition of semiholonomic jets.

How to cite

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Cabras, Antonella, and Kolář, Ivan. "Prolongation of projectable tangent valued forms." Archivum Mathematicum 038.4 (2002): 243-257. <http://eudml.org/doc/248940>.

@article{Cabras2002,
abstract = {First we deduce some general properties of product preserving bundle functors on the category of fibered manifolds. Then we study the prolongation of projectable tangent valued forms with respect to these functors and describe the complete lift of the Frölicher-Nijenhuis bracket. We also present the coordinate formula for composition of semiholonomic jets.},
author = {Cabras, Antonella, Kolář, Ivan},
journal = {Archivum Mathematicum},
keywords = {projectable tangent valued form; product preserving bundle functor; jet; Weil bundle; Frölicher-Nijenhuis bracket; projectable tangent valued form; product preserving bundle functor; jet; Weil bundle; Frölicher-Nijenhuis bracket},
language = {eng},
number = {4},
pages = {243-257},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Prolongation of projectable tangent valued forms},
url = {http://eudml.org/doc/248940},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Cabras, Antonella
AU - Kolář, Ivan
TI - Prolongation of projectable tangent valued forms
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 4
SP - 243
EP - 257
AB - First we deduce some general properties of product preserving bundle functors on the category of fibered manifolds. Then we study the prolongation of projectable tangent valued forms with respect to these functors and describe the complete lift of the Frölicher-Nijenhuis bracket. We also present the coordinate formula for composition of semiholonomic jets.
LA - eng
KW - projectable tangent valued form; product preserving bundle functor; jet; Weil bundle; Frölicher-Nijenhuis bracket; projectable tangent valued form; product preserving bundle functor; jet; Weil bundle; Frölicher-Nijenhuis bracket
UR - http://eudml.org/doc/248940
ER -

References

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  9. Torsion of connections on tangent bundles of higher order, Supplemento ai Rendiconti Palermo, Série II, No 54 (1997), 65–73. MR1662727
  10. Graded Lie algebras and connections on a fibered space, J. Math. pures et appl. 63 (1984), 111–120. MR0776913
  11. Product preserving bundle functors on fibered manifolds, Archivum Math. (Brno) 32 (1996), 307–316. Zbl0881.58002MR1441401
  12. Differential calculus on fibred manifolds, manuscript, 2000. Zbl0841.53023
  13. Natural operators transforming projectable vector fields to product preserving bundles, Supplemento ai Rendiconti Palermo, Série II, No 59 (1999), 181–187. MR1692269
  14. Théorie des points proches sur les variétés différentielles, Colloque de topol. et géom. diff., Strasbourg (1953), 111–117. MR0061455

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