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This is a Quantitative Study study.

October 1, 2025Open Access

Lie derivatives of sections of natural vector bundles

Key Points

Lie derivatives express time derivative relationships in natural vector bundles, revealing deeper geometric connections.
The study computes derivatives using adapted non-autonomous vector fields, enhancing understanding of vector bundle behavior.
The analysis builds on established lemmas concerning flows and fields, expanding upon classic results in differential geometry.
These findings could inspire new applications in theoretical physics and advanced mathematics, unlocking complex geometrical frameworks.

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 This Study

Peter W. Michor (Tue,) studied this question.

synapsesocial.com/papers/68dd91c7fe798ba2fc49859f https://doi.org/https://doi.org/10.48550/arxiv.2504.15605

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