Complete connections on fiber bundles
arXiv:1512.03847 · doi:10.1016/j.indag.2016.06.009
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.
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)