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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 〔Let us recall that Ricci scalar is linear in the second derivatives of the metric tensor , quadratic in the first derivatives and contains the inverse matrix which is a rational function of the components .〕 is the only scalar invariant (or absolute invariant) linear in the second derivatives of the metric tensor .
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Vermeil's theorem」の詳細全文を読む
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