Covariant derivatives for Ehresmann connections
Differential Geometry
2022-05-25 v2 Mathematical Physics
math.MP
Abstract
We deal with the construction of covariant derivatives for some quite general Ehresmann connections on fibre bundles. We show how the introduction of a vertical endomorphism allows construction of covariant derivatives separately on both the vertical and horizontal distributions of the connection which can then be glued together on the total space. We give applications across an important class of tangent bundle cases, frame bundles and the Hopf bundle.
Keywords
Cite
@article{arxiv.2110.07242,
title = {Covariant derivatives for Ehresmann connections},
author = {G. E. Prince and D. J. Saunders},
journal= {arXiv preprint arXiv:2110.07242},
year = {2022}
}