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arXiv · 2106.16141

Leafwise flat forms on Inoue-Bombieri surfaces

Daniele Angella·Valentino Tosatti
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Abstract

We prove that every Gauduchon metric on an Inoue-Bombieri surface admits a strongly leafwise flat form in its $\partial\overline\partial$-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 $\partial\overline\partial$-class of the Tricerri/Vaisman metric.

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Daniele Angella, Valentino Tosatti. 2021-06-30. Leafwise flat forms on Inoue-Bombieri surfaces. https://doi.org/10.1016/j.jfa.2023.110015

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