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  "body": "\n## Summary\n\nParallel transport moves vectors along a curve in a manifold while keeping them \"constant\" in the sense of a given [[connection|5ZYRRVE8BW]].\nIt gives, for each curve, a linear isomorphism between the fibres over its endpoints.\nThe result usually depends on the curve, not only on its endpoints, and this dependence is measured by curvature and holonomy.\nA connection can be recovered from its parallel transports, so the two describe the same data.\n\n## Explanations\n\n### L1 human\n\nWalk along a path on a surface carrying a spear, and never turn the spear relative to the surface as you go.\nWhere the spear ends up pointing is the parallel transport of its starting direction.\nOn a flat plane the spear always points the same way, whatever path you take.\nOn a sphere, walk from the north pole down to the equator, a quarter of the way around the equator, and back to the pole.\nThe spear comes back turned by a right angle, which shows that the sphere is curved.\n",
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