Is there a way to define the Taylor expansion of a function $f:\mathcal{M}\rightarrow\mathbb{R}$, where $\mathcal{M}$ is a smooth manifold? I'm looking for a free coordinate definition. I guess it is necessary to equip $\mathcal{M}$ with a linear connection (covariant derivative).
2026-04-04 13:48:46.1775310526
Taylor expansion on a Manifold
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