Connections from trivializations

Jan Kurek, Włodzimierz Mikulski


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.


Gauge natural bundle; gauge natural operator; principal connection

Full Text:



Dębecki, J., Affine liftings of torsion-free connections to Weil bundles, Colloq. Math. 114 (1) (2009), 1-8.

Doupovec, M., Mikulski, W. M., Reduction theorems for principal and classical connections, Acta Math. Sinica (E-S) 26 (1) (2010), 169-184.

Janyska, J., Vondra, J., Natural principal connections on the principal gauge prolongation of the principal bundle, Rep. Math. Phys. 64 (3) (2009), 395-415.

Kobayashi, S., Nomizu, K., Foundations of Differential Geometry. Vol I, J. Wiley-Interscience, New York-London, 1963.

Kolar, I., Induced connections on total spaces of fiber bundles, Int. J. Geom. Methods Mod. Phys. 7 (4) (2010), 705-711.

Kolar, I., Michor, P. W., Slovak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.

Data publikacji: 2016-12-24 22:42:02
Data złożenia artykułu: 2016-12-23 21:54:30


  • There are currently no refbacks.

Copyright (c) 2016 Jan Kurek, Włodzimierz Mikulski