Abstract
In this section we define the notion of an Ehresmann connection associated to a surjective submersion \( \pi :M \to N \). A connection permits a curve in N to be locally lifted to a horizontal curve in M. An Ehresmann connection is good if every smooth curve in N has a global horizontal lift. For good connections we define the notions of parallel translation and holonomy.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer Basel
About this chapter
Cite this chapter
Cushman, R.H., Bates, L.M. (2015). Ehresmann connections. In: Global Aspects of Classical Integrable Systems. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0918-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0918-4_8
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0917-7
Online ISBN: 978-3-0348-0918-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)