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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 Sasakian manifold ： ウィキペディア英語版 Sasakian manifold In differential geometry, a Sasakian manifold (named after Shigeo Sasaki) is a contact manifold $(M,\backslash theta)$ equipped with a special kind of Riemannian metric $g$, called a ''Sasakian'' metric. ==Definition== A Sasakian metric is defined using the construction of the ''Riemannian cone''. Given a Riemannian manifold $(M,g)$, its Riemannian cone is a product :$(M\backslash times\; ^)\backslash ,$ of $M$ with a half-line $^$, equipped with the ''cone metric'' :$t^2\; g\; +\; dt^2,\backslash ,$ where $t$ is the parameter in $^$. A manifold $M$ equipped with a 1-form $\backslash theta$ is contact if and only if the 2-form :$t^2\backslash ,d\backslash theta\; +\; 2t\backslash ,\; dt\; \backslash cdot\; \backslash theta\backslash ,$ on its cone is symplectic (this is one of the possible definitions of a contact structure). A contact Riemannian manifold is Sasakian, if its Riemannian cone with the cone metric is a Kähler manifold with Kähler form :$t^2\backslash ,d\backslash theta\; +\; 2t\backslash ,dt\; \backslash cdot\; \backslash theta.\backslash ,$ 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「Sasakian manifold」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.