Connections from trivializations

Jan Kurek; Włodzimierz Mikulski

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2016)

  • Volume: 70, Issue: 2
  • ISSN: 0365-1029

Abstract

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Let P be a principal fiber bundle with the basis M and with the structural group G. A trivialization of P is a section of P. It is proved that there exists only one gauge natural operator transforming trivializations of P into principal connections in P. All gauge natural operators transforming trivializations of P and torsion free classical linear connections on M into classical linear connections on P are completely described.

How to cite

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Jan Kurek, and Włodzimierz Mikulski. "Connections from trivializations." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 70.2 (2016): null. <http://eudml.org/doc/289844>.

@article{JanKurek2016,
abstract = {Let P be a principal fiber bundle with the basis M and with the structural group G. A trivialization of P is a section of P. It is proved that there exists only one gauge natural operator transforming trivializations of P into principal connections in P. All gauge natural operators transforming trivializations of P and torsion free classical linear connections on M into classical linear connections on P are completely described.},
author = {Jan Kurek, Włodzimierz Mikulski},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Gauge natural bundle; gauge natural operator; principal connection},
language = {eng},
number = {2},
pages = {null},
title = {Connections from trivializations},
url = {http://eudml.org/doc/289844},
volume = {70},
year = {2016},
}

TY - JOUR
AU - Jan Kurek
AU - Włodzimierz Mikulski
TI - Connections from trivializations
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2016
VL - 70
IS - 2
SP - null
AB - Let P be a principal fiber bundle with the basis M and with the structural group G. A trivialization of P is a section of P. It is proved that there exists only one gauge natural operator transforming trivializations of P into principal connections in P. All gauge natural operators transforming trivializations of P and torsion free classical linear connections on M into classical linear connections on P are completely described.
LA - eng
KW - Gauge natural bundle; gauge natural operator; principal connection
UR - http://eudml.org/doc/289844
ER -

References

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  1. Dębecki, J., Affine liftings of torsion-free connections to Weil bundles, Colloq. Math. 114 (1) (2009), 1-8. 
  2. Doupovec, M., Mikulski, W. M., Reduction theorems for principal and classical connections, Acta Math. Sinica (E-S) 26 (1) (2010), 169-184. 
  3. Janyska, J., Vondra, J., Natural principal connections on the principal gauge prolongation of the principal bundle, Rep. Math. Phys. 64 (3) (2009), 395-415. 
  4. Kobayashi, S., Nomizu, K., Foundations of Differential Geometry. Vol I, J. Wiley-Interscience, New York-London, 1963. 
  5. Kolar, I., Induced connections on total spaces of fiber bundles, Int. J. Geom. Methods Mod. Phys. 7 (4) (2010), 705-711. 
  6. Kolar, I., Michor, P. W., Slovak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. 

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