Leafwise flat forms on Inoue-Bombieri surfaces
Leafwise flat forms on Inoue-Bombieri surfaces
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DOI：
10.1016/j.jfa.2023.110015
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发表时间：
2021-06
影响因子：
1.7
通讯作者：
Daniele Angella;Valentino Tosatti
中科院分区：
文献类型：
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作者：
Daniele Angella;Valentino Tosatti
我们证明了Inoue-Bombieri曲面上的每一个Gauduchon度量在它的∂∂‾类中都有一个强叶平坦形式。利用这一结果，我们得到了归一化的Chern-Ricci流在所有Inoue-Bombieri曲面上以任意Gauduchon度量开始的一致收敛。我们还证明了在∂∂‾类的Tricerri/Vaisman度量下，初始度量的收敛是光滑的且曲率有界。
We prove that every Gauduchon metric on an Inoue-Bombieri surface admits a strongly leafwise flat form in its∂∂‾-class. Using this result, we deduce uniform convergence of the normalized Chern-Ricci flow starting at any Gauduchon metric on all Inoue-Bombieri surfaces. We also show that the convergence is smooth with bounded curvature for initial metrics in the∂∂‾-class of the Tricerri/Vaisman metric.