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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 Eells–Kuiper manifold ： ウィキペディア英語版 Eells–Kuiper manifold In mathematics, an Eells–Kuiper manifold is a compactification of $R^n$ by an $\backslash frac$ - sphere, where ''n'' = 2, 4, 8, or 16. It is named after James Eells and Nicolaas Kuiper. If ''n'' = 2, the Eells–Kuiper manifold is diffeomorphic to the real projective plane $RP(2)$. For $n\backslash ge\; 4$ it is simply-connected and has the integral cohomology structure of the complex projective plane $CP^2$ ($n\; =\; 4$), of the quaternionic projective plane $HP^2$ ($n\; =\; 8$) or of the Cayley projective plane (''n'' = 16). ==Properties== These manifolds are important in both Morse theory and foliation theory: Theorem:〔.〕 ''Let $M$ be a connected closed manifold (not necessarily orientable) of dimension $n$. Suppose $M$ admits a Morse function $f:M\backslash to\; R$ of class $C^3$ with exactly three singular points. Then $M$ is a Eells–Kuiper manifold.'' Theorem:〔.〕 ''Let $M^n$ be a compact connected manifold and $F$ a Morse foliation on $M$. Suppose the number of centers $c$ of the foliation $F$ is more than the number of saddles $s$. Then there are two possibilities:'' * ''$c=s+2$, and $M^n$ is homeomorphic to the sphere $S^n$'', * ''$c=s+1$, and $M^n$ is an Eells—Kuiper manifold, $n=2,4,8$ or $16$.'' 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「Eells–Kuiper 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.