Lie derivatives of sections of natural vector bundles
Differential Geometry
2025-04-23 v1
Abstract
Time derivatives of pullbacks and push forwards along smooth curves of diffeomorphism of sections of natural vector bundles are computed in terms of Lie derivatives along adapted non-autonomous vector fields by extending a key lemma in [Markus Mauhart, Peter W. Michor: Commutators of flows and fields. Arch. Math. (Brno) 28 (1992), 228-236. arXiv:math/9204221]. There is also the analogous result about the first non-vanishing derivative of higher order.
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Cite
@article{arxiv.2504.15605,
title = {Lie derivatives of sections of natural vector bundles},
author = {Peter W. Michor},
journal= {arXiv preprint arXiv:2504.15605},
year = {2025}
}
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6 pages