Complete connections on fiber bundles
Differential Geometry
2017-01-11 v2
Abstract
Every smooth fiber bundle admits a complete (Ehresmann) connection. This result appears in several references, with a proof on which we have found a gap, that does not seem possible to remedy. In this note we provide a definite proof for this fact, explain the problem with the previous one, and illustrate with examples. We also establish a version of the theorem involving Riemannian submersions.
Cite
@article{arxiv.1512.03847,
title = {Complete connections on fiber bundles},
author = {Matias del Hoyo},
journal= {arXiv preprint arXiv:1512.03847},
year = {2017}
}
Comments
5 pages. Revised version. A misleading typo on the proof of the main theorem is fixed (the open W_i should be defined by using V_i instead of U_i)