The pluriclosed flow for T²-invariant Vaisman metrics on the Kodaira-Thurston surface

2023/09/27 by Fino, Anna, Grantcharov, Gueo, Perez, Eddy · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.15937

Abstract

In this note we study T²-invariant pluriclosed metrics on the Kodaira-Thurston surface. We obtain a characterization of T²-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 T²-invariant Vaisman metric, then the pluriclosed flow preserves the Vaisman condition, extending to the non-constant scalar curvature case the previous results in [6].

Cited by

• Pluriclosed flow on Oeljeklaus-Toma manifolds

Related

• The pluriclosed flow and the Vaisman condition
• A parabolic flow of pluriclosed metrics
• Vaisman manifolds and transversally Kähler-Einstein metrics
• Ambient Obstruction Flow
• Horocycle flow on negative variable curvature surface is standard