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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 Inoue surface ： ウィキペディア英語版 Inoue surface In complex geometry, a part of mathematics, the term Inoue surface denotes several complex surfaces of Kodaira class VII. They are named after Masahisa Inoue, who gave the first non-trivial examples of Kodaira class VII surfaces in 1974.〔M. Inoue, ''On surfaces of class VII0,'' Inventiones math., 24 (1974), 269–310.〕 The Inoue surfaces are not Kähler manifolds. ==Inoue surfaces with ''b''2 = 0== Inoue introduced three families of surfaces, ''S''0, ''S''+ and ''S''−, which are compact quotients of $\backslash times\; H$ (a product of a complex plane by a half-plane). These Inoue surfaces are solvmanifolds. They are obtained as quotients of $\backslash times\; H$ by a solvable discrete group which acts holomorphically on $\backslash times\; H$. The solvmanifold surfaces constructed by Inoue all have second Betti number $b\_2=0$. These surfaces are of Kodaira class VII, which means that they have $b\_1=1$ and Kodaira dimension $-\backslash infty$. It was proven by Bogomolov,〔Bogomolov, F.: ''Classification of surfaces of class VII0 with ''b''2 = 0, Math. USSR Izv 10, 255–269 (1976)〕 Li-Yau 〔Li, J., Yau, S., T.: ''Hermitian Yang-Mills connections on non-Kahler manifolds,'' Math. aspects of string theory (San Diego, Calif., 1986), Adv. Ser. Math. Phys. 1, 560–573, World Scientific Publishing (1987)〕 and Teleman〔Teleman, A.: ''Projectively flat surfaces and Bogomolov's theorem on class VII0-surfaces'', Int. J. Math., Vol. 5, No 2, 253–264 (1994)〕 that any surface of class VII with ''b''2 = 0 is a Hopf surface or an Inoue-type solvmanifold. These surfaces have no meromorphic functions and no curves. K. Hasegawa 〔Keizo Hasegawa (''Complex and Kahler structures on Compact Solvmanifolds,'' ) J. Symplectic Geom. Volume 3, Number 4 (2005), 749–767.〕 gives a list of all complex 2-dimensional solvmanifolds; these are complex torus, hyperelliptic surface, Kodaira surface and Inoue surfaces ''S''0, ''S''+ and ''S''−. The Inoue surfaces are constructed explicitly as follows.〔 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「Inoue surface」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.