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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 Conformal Killing equation ： ウィキペディア英語版 Conformal Killing equation In conformal geometry, the conformal Killing equation on a manifold of space-dimension ''n'' with metric $g$ describes those vector fields $X$ which preserve $g$ up to scale, i.e. :$\backslash mathcal\_g\; =\; \backslash lambda\; g$ for some function $\backslash lambda$ (where $\backslash mathcal\_$ is the Lie derivative). Vector fields that satisfy the conformal Killing equation are exactly those vector fields whose flow preserves the conformal structure of the manifold. The name Killing refers to Wilhelm Killing, who first investigated the Killing equation for vector fields that preserve a Riemannian metric. By taking the trace we find that necessarily $\backslash lambda\; =\; \backslash frac\backslash mathrmX$. Therefore we can write the conformal Killing equation as :$\backslash left(\backslash mathcal\_X\; -\; \backslash frac\backslash right)g=0.$ In abstract indices, :$\backslash nabla\_X\_\; -\backslash fracg\_\backslash nabla\_X^=0,$ where the round brackets denote symmetrization. For any but 2, there is a finite number of solutions, specifying the conformal symmetry of that space, but in two dimensions, there is an infinity of solutions. ==See also== *Einstein manifold * invariant differential operator 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「Conformal Killing equation」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.