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Vermeil's theorem : ウィキペディア英語版
Vermeil's theorem
In differential geometry, Vermeil's theorem essentially states that 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.
== Standard version of the theorem ==
The theorem states that the Ricci scalar R〔Let us recall that Ricci scalar R is linear in the second derivatives of the metric tensor g_, quadratic in the first derivatives and contains the inverse matrix g^, which is a rational function of the components g_.〕 is the only scalar invariant (or absolute invariant) linear in the second derivatives of the metric tensor g_.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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