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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 First variation of area formula ： ウィキペディア英語版 First variation of area formula In Riemannian geometry, the first variation of area formula relates the mean curvature of a hypersurface to the rate of change of its area as it evolves in the outward normal direction. Let $\backslash Sigma(t)$ be a smooth family of oriented hypersurfaces in a Riemannian manifold ''M'' such that the velocity of each point is given by the outward unit normal at that point. The first variation of area formula is :$\backslash frac\backslash ,\; dA\; =\; H\; \backslash ,dA,$ where ''dA'' is the area form on $\backslash Sigma(t)$ induced by the metric of ''M'', and ''H'' is the mean curvature of $\backslash Sigma(t)$. The normal vector is parallel to $D\_\; \backslash vec\_$ where $\backslash vec\_$ is the tangent vector. The mean curvature is parallel to the normal vector. ==References== *Chow, Lu, and Ni, "Hamilton's Ricci Flow." AMS Science Press, GSM volume 77, 2006. 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「First variation of area formula」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.