On the existence of Kähler metrics of constant scalar curvature
On the existence of Kähler metrics of constant scalar curvature
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DOI：
10.2748/tmj/1245849446
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发表时间：
2009-02
影响因子：
0.5
通讯作者：
K. Tsuboi
中科院分区：
文献类型：
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作者：
K. Tsuboi
.对于具有全纯向量场约化李代数的紧致复Fano流形M，我们确定了M的第二上同调群的解析子簇，该群由Bando-Calabi-Futaki特征标为零的Kähler类组成.然后一个Kähler类包含一个常数量曲率的Kähler度量当且仅当Kähler类包含在解析子簇中。通过对解析子簇的研究，证明了M允许有无限多个非位似的Kähler类包含常数量曲率的Kähler度量，但不允许任何Kähler-Einstein度量。
. For certain compact complex Fano manifolds M with reductive Lie algebras of holomorphic vector fields, we determine the analytic subvariety of the second cohomology group of M consisting of Kähler classes whose Bando-Calabi-Futaki character vanishes. Then a Kähler class contains a Kähler metric of constant scalar curvature if and only if the Kähler class is contained in the analytic subvariety. On examination of the analytic subvariety, it is shown that M admits infinitely many nonhomothetic Kähler classes containing Kähler metrics of constant scalar curvature but does not admit any Kähler-Einstein metric.