Frame bundle
= Frame bundle
{title2=$\operatorname{Fr}(TM)$}
The frame bundle of an $n$-dimensional <smooth manifold> has fiber over $x$ consisting of linear <isomorphisms> $u:\mathbb R^n\to T_xM$. Right composition by $GL(n,\mathbb R)$ makes it a <principal bundle>. A global <frame of a vector bundle> is a global <section of a fiber bundle> and trivializes the <tangent bundle>. A metric restricts the allowed frames to the <orthonormal frame bundle>.