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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 Systoles of surfaces ： ウィキペディア英語版 Systoles of surfaces In mathematics, systolic inequalities for curves on surfaces were first studied by Charles Loewner in 1949 (unpublished; see remark at end of P. M. Pu's paper in '52). Given a closed surface, its systole, denoted sys, is defined to the least length of a loop that cannot be contracted to a point on the surface. The ''systolic area'' of a metric is defined to be the ratio area/sys2. The ''systolic ratio'' SR is the reciprocal quantity sys2/area. See also Introduction to systolic geometry. ==Torus== In 1949 Loewner proved his inequality for metrics on the torus T2, namely that the systolic ratio SR(T2) is bounded above by $2/\backslash sqrt$, with equality in the flat (constant curvature) case of the equilateral torus (see hexagonal lattice). 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「Systoles of surfaces」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.