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 Albert Einstein’s theory of General Relativity. The theorem was proved by the German mathematician Hermann Vermeil in 1917.

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