Vermeil's theorem

In differential geometry, Vermeil's theorem essentially states that the scalar curvature is the only (non-trivial) absolute invariant among those of prescribed type suitable for Einstein’s theory. The theorem was proved by the German mathematician Hermann Vermeil in 1917.

The theorem states that the Ricci scalar ${\displaystyle R}$ is the only scalar invariant (or absolute invariant) linear in the second derivatives of the metric tensor ${\displaystyle g_{\mu \nu }}$.

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