# American Institute of Mathematical Sciences

June  2016, 8(2): 199-220. doi: 10.3934/jgm.2016004

## Infinitesimally natural principal bundles

 1 Universiteit Utrecht, Budapestlaan 6, 3584 CD Utrecht, Netherlands

Received  June 2015 Revised  April 2016 Published  June 2016

We extend the notion of a natural fibre bundle by requiring diffeomorphisms of the base to lift to automorphisms of the bundle only infinitesimally, i.e. at the level of the Lie algebra of vector fields. We classify the principal fibre bundles with this property. A version of the main result in this paper (theorem 4.4) can be found in Lecomte's work [12]. Our approach was developed independently, uses the language of Lie algebroids, and can be generalized in several directions.
Citation: Bas Janssens. Infinitesimally natural principal bundles. Journal of Geometric Mechanics, 2016, 8 (2) : 199-220. doi: 10.3934/jgm.2016004
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##### References:
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