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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 Ricci soliton ： ウィキペディア英語版 Ricci soliton In differential geometry, a Ricci soliton is a special type of Riemannian metric. Such metrics evolve under Ricci flow only by symmetries of the flow, and they can be viewed as generalizations of Einstein metrics. The concept is named after Gregorio Ricci-Curbastro. Ricci flow solutions are invariant under diffeomorphisms and scaling, so one is led to consider solutions that evolve exactly in these ways. A metric $g\_0$ on a smooth manifold $M$ is a Ricci soliton if there exists a function $\backslash sigma(t)$ and a family of diffeomorphisms $\backslash \; \backslash subset\; \backslash operatorname(M)$ such that :$g(t)\; =\; \backslash sigma(t)\; \backslash ,\; \backslash eta(t)^$ * g_0 is a solution of Ricci flow. In this expression, $\backslash eta(t)^$ *g_0 refers to the pullback off the metric $g\_0$ by the diffeomorphism $\backslash eta(t)$. Equivalently, a metric $g\_0$ is a Ricci soliton if and only if :$\backslash operatorname(g\_0)\; =\; \backslash lambda\; \backslash ,\; g\_0\; +\; \backslash mathcal\_X\; g\_0,$ where $\backslash operatorname$ is the Ricci curvature tensor, $\backslash lambda\; \backslash in\; \backslash mathbb$, $X$ is a vector field on $M$, and $\backslash mathcal$ represents the Lie derivative. This condition is a generalization of the Einstein condition for metrics: :$\backslash operatorname(g\_0)\; =\; \backslash lambda\; \backslash ,\; g\_0.$ ==References== * 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「Ricci soliton」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.