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The pluriclosed flow for $T^2$-invariant Vaisman metrics on the Kodaira-Thurston surface. (arXiv:2309.15937v1 [math.DG]) http://arxiv.org/abs/2309.15937

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

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].

arxiv.org
September 29, 2023 at 3:10 AM · · feed2toot · 0 · 0 · 0
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