If I'm considering a parallelizable Riemannian manifold $M$ we have that the frame bundle has some structure group $G$. Is the group relating all possible global trivializations of the frame bundle still $G$? I would expect it to be maybe more restricted than the structure group linking arbitrary local trivializations on $M$.
2026-03-30 20:47:41.1774903661
Structure group relating global cross sections of frame bundle.
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