On the metric structure of non-Kähler complex surfaces
On the metric structure of non-Kähler complex surfaces
复制标题
非凯勒复曲面的度量结构
DOI：
10.1007/s002080050357
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发表时间：
2000
影响因子：
1.4
通讯作者：
F. Belgun
中科院分区：
文献类型：
--
作者：
F. Belgun
给出了局部共形Kähler(l.c.K.)紧致复曲面上具有平行Lee形式的度量。利用曲面的Kodaira分类，我们对允许这种结构的紧致复杂曲面进行了分类。这给出了紧致三维流形上的Sasakian结构的分类。上述刻划的一个弱版本导致了所有Hopf曲面上L.C.K.度量的显式构造。刻画了几何复曲面上的局部齐次L.C.K.度量，并证明了某些Inoue曲面不允许任何L.C.K.度量。
We give a characterization of a locally conformally Kähler (l.c.K.) metric with parallel Lee form on a compact complex surface. Using the Kodaira classification of surfaces, we classify the compact complex surfaces admitting such structures. This gives a classification of Sasakian structures on compact three-manifolds. A weak version of the above mentioned characterization leads to an explicit construction of l.c.K. metrics on all Hopf surfaces. We characterize the locally homogeneous l.c.K. metrics on geometric complex surfaces, and we prove that some Inoue surfaces do not admit any l.c.K. metric.