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arXiv · 1512.03847

Complete connections on fiber bundles

Matias del Hoyo
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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.

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Matias del Hoyo. 2017-01-10. Complete connections on fiber bundles. https://doi.org/10.1016/j.indag.2016.06.009

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