Homogeneous Solutions of Pluriclosed Flow on Closed Complex Surfaces

Abstract

Streets and Tian introduced a parabolic flow of pluriclosed metrics. We classify the long time behavior of homogeneous solutions of this flow on closed complex surfaces including minimal Hopf, Inoue, Kodaira, and non-Kahler, properly elliptic surfaces. We also construct expanding soliton solutions to the flow on the universal covers of these surfaces by taking blowdown limits of these homogeneous solutions.

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References in corpus (1)

• The Chern-Ricci flow on complex surfaces

Cited by in corpus (5)

• The long-time behavior of the homogeneous pluriclosed flow
• Hermitian Curvature flow on unimodular Lie groups and static invariant metrics
• A remark on the Bismut-Ricci form on 2-step nilmanifolds
• Hermitian curvature flow on complex locally homogeneous surfaces
• Positive Hermitian Curvature Flow on nilpotent and almost-abelian complex Lie groups