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  "body": "\n## Summary\n\nThe Weyl tensor is defined on a [[pseudo-Riemannian manifold|GH6CXWFNDJ]] of dimension at least $3$.\nIt is the part of the [[Riemann curvature tensor|JA29ETCM02]] left after removing all that the [[Ricci curvature|4GTNM0WHDH]] determines.\nIt is unchanged, as a $(1,3)$-tensor, when the metric is multiplied by a positive function, so it measures conformal geometry.\nIn dimension at least $4$, it vanishes exactly when the metric is locally conformally flat.\nIn general relativity it describes tidal forces and gravitational waves in vacuum.\n\n## Explanations\n\n### L1 human\n\nCurvature in several dimensions has many components.\nSome of them say how volumes change, and these are captured by the Ricci curvature.\nThe rest say how shapes are distorted without changing volume, and that rest is the Weyl tensor.\nA round sphere has zero Weyl tensor, because it can be mapped to flat space by a map that keeps angles, the stereographic projection.\n",
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