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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 G2 manifold ： ウィキペディア英語版 G2 manifold In differential geometry, a ''G''2 manifold is a seven-dimensional Riemannian manifold with holonomy group contained in ''G''2. The group $G\_2$ is one of the five exceptional simple Lie groups. It can be described as the automorphism group of the octonions, or equivalently, as a proper subgroup of special orthogonal group SO(7) that preserves a spinor in the eight-dimensional spinor representation or lastly as the subgroup of the general linear group GL(7) which preserves the non-degenerate 3-form $\backslash phi$, the associative form. The Hodge dual, $\backslash psi=$ *\phi is then a parallel 4-form, the coassociative form. These forms are calibrations in the sense of Harvey–Lawson, and thus define special classes of 3- and 4-dimensional submanifolds. == Properties == If ''M'' is a $G\_2$-manifold, then ''M'' is: * Ricci-flat, * orientable, * a spin manifold. 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「G2 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.