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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hitchin–Thorpe inequality ： ウィキペディア英語版 Hitchin–Thorpe inequality In differential geometry the Hitchin–Thorpe inequality is a relation which restricts the topology of 4-manifolds that carry an Einstein metric. == Statement of the Hitchin–Thorpe inequality == Let ''M'' be a compact, oriented, smooth four-dimensional manifold. If there exists a Riemannian metric on ''M'' which is an Einstein metric, then following inequality holds : $\backslash chi(M)\; \backslash geq\; \backslash frac|\backslash tau(M)|,$ where $\backslash chi(M)$ is the Euler characteristic of $M$ and $\backslash tau(M)$ is the signature of $M$. This inequality was first stated by John Thorpe〔J. Thorpe, ''Some remarks on the Gauss-Bonnet formula'', J. Math. Mech. 18 (1969) pp. 779--786.〕 in a footnote to a 1969 paper focusing on manifolds of higher dimension. Nigel Hitchin then rediscovered the inequality, and gave a complete characterization 〔N. Hitchin, ''On compact four-dimensional Einstein manifolds'', J. Diff. Geom. 9 (1974) pp. 435--442.〕 of the equality case in 1974; he found that if $(M,g)$ is an Einstein manifold with $\backslash chi(M)\; =\; \backslash frac|\backslash tau(M)|,$ then $(M,g)$ must be a flat torus, a Calabi–Yau manifold, or a quotient thereof. 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「Hitchin–Thorpe inequality」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.