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arXiv · 2309.15937

The pluriclosed flow for $T^2$-invariant Vaisman metrics on the Kodaira-Thurston surface

Anna Fino·Gueo Grantcharov·Eddy Perez
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Abstract

In this note we study $T^2$-invariant pluriclosed metrics on the Kodaira-Thurston surface. We obtain a characterization of $T^2$-invariant Vaisman metrics, and notice that the Kodaira-Thurston surface admits Vaisman metrics with non-constant scalar curvature. Then we study the behaviour of the Vaisman condition in relation to the pluriclosed flow. As a consequence, we show that if the initial metric on the Kodaira-Thurston surface is a $T^2$-invariant Vaisman metric, then the pluriclosed flow preserves the Vaisman condition, extending to the non-constant scalar curvature case the previous results in [6].

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Anna Fino, Gueo Grantcharov, Eddy Perez. 2023-09-27. The pluriclosed flow for $T^2$-invariant Vaisman metrics on the Kodaira-Thurston surface. https://arxiv.org/abs/2309.15937

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