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  "body": "\n## Summary\n\nThe frame bundle of a manifold is the space of all ordered bases of all tangent spaces.\nA point of it is a point of the manifold together with a choice of coordinate axes for the tangent space there.\nThe general linear group acts on it by changing the basis, which makes it a principal bundle.\nIt is the natural home of connections and of G-structures, such as Riemannian metrics and orientations.\n\n## Explanations\n\n### L1 human\n\nAt each point of a surface you can draw two arrows tangent to it that are not parallel; they form a frame.\nThe frame bundle collects all possible frames at all points.\nTwo frames at the same point differ by an invertible $2 \\times 2$ matrix.\nIf you only allow perpendicular arrows of unit length, you get the smaller orthonormal frame bundle.\n",
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