Given a Riemannian manifold $(M,g)$, is the holonomy group of $g$ the structure group of the oriented tangent bundle on $M$? If not, is there a relation between the two? Their definitions seem quite similar (possibly identical) to me, but perhaps I'm missing something.
2026-03-26 01:07:37.1774487257
Holonomy vs structure group of tangent bundle
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