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arXiv · 2607.26890

The Lie algebra generated by gradient vector fields

Bettina Kazandjian·Omar Mohsen·Eugenio Pozzoli
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Abstract

Let $M$ be a smooth compact manifold, and $g$ a smooth non-degenerate symmetric bilinear form on $TM$. We prove that every smooth vector field can be written as a finite linear combination of iterated Lie brackets of gradient vector fields.

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Bettina Kazandjian, Omar Mohsen, Eugenio Pozzoli. 2026-07-29. The Lie algebra generated by gradient vector fields. https://arxiv.org/abs/2607.26890

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