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This topic has appeared in the English Wikipedia rankings 1 time. It first appeared on 2026-08-23 and was most recently seen on 2026-08-23.
In differential geometry, the Cotton tensor on a pseudo-Riemannian manifold of dimension n is a third-order tensor concomitant of the metric tensor. The vanishing of the Cotton tensor for n = 3 is necessary and sufficient condition for the manifold to be locally conformally flat. By contrast, in dimensions n ≥ 4, the vanishing of the Cotton tensor is necessary but not sufficient for the metric to be conformally flat; instead, the corresponding necessary and sufficient condition in these higher dimensions is the vanishing of the Weyl tensor, while the Cotton tensor just becomes a constant times the divergence of the Weyl tensor. For n < 3 the Cotton tensor is identically zero. The concept is named after Émile Cotton.
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