A Kummer type construction of self-dual metrics on the connected sum of four complex projective planes
A Kummer type construction of self-dual metrics on the connected sum of four complex projective planes
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四个复射影平面连通和上的自对偶度量的 Kummer 型构造
DOI：
10.2969/jmsj/05210139
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发表时间：
2000
影响因子：
0.7
通讯作者：
M. Itoh
中科院分区：
文献类型：
--
作者：
N. Honda;M. Itoh
.我们证明了在4个复射影平面的连通和CP 2上存在自对偶度量，该度量具有以下性质：（i）标量曲率的符号是正的，（ii）等距群的单位分量是U. 1 <$，（iii）该度量与LeBrun [LB 1]构造的自对偶度量不是共形等距的.这些是单连通流形上具有非半自由U... 1 <$<$等距的自对偶度量的第一个例子。我们的证明是基于扭量理论：我们使用的唐纳森和弗里德曼[ DF ]的建设等变orbifold版本。我们也给出了相应扭量空间的代数约化的结构的粗略描述。
. We show that there exist on 4 CP 2 , the connected sum of four complex projective planes, self-dual metrics with the following properties: (i) the sign of the scalar curvature is positive, (ii) the identity component of the isometry group is U … 1 † , (iii) the metrics are not conformally isometric to the self-dual metrics constructed by LeBrun [ LB1 ]. These are the ®rst examples of self-dual metrics with non semi-free U … 1 † isometries on simply connected manifolds. Our proof is based on the twistor theory: we use an equivariant orbifold version of the construction of Donaldson and Friedman [ DF ]. We also give a rough description of the structure of the algebraic reduction of the corresponding twistor spaces.
三重紧凑复杂空间的唐纳森-弗里德曼构造和变形
DOI：
--
发表时间：
2003
期刊：
Math.Nachrichten 256
影响因子：
--
作者：
Y.Sakane;T.Yamada;N.Honda;Y.Namikawa;N.Honda
通讯作者：
N.Honda