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<p>In this paper, we introduce the Calabi flow on a compact, quasi-Kähler manifold and provide a priori estimates along the flow under the assumption of a uniform bound on the Chern scalar curvature of the evolving metric. Using these estimates, we show that if the Chern scalar curvature is uniformly bounded for all time, then the flow converges smoothly to the unique Chern–Ricci-flat metric in almost Hermitian geometry.</p>

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On the Calabi flow on quasi-Kähler manifolds

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Masaya Kawamura

摘要

In this paper, we introduce the Calabi flow on a compact, quasi-Kähler manifold and provide a priori estimates along the flow under the assumption of a uniform bound on the Chern scalar curvature of the evolving metric. Using these estimates, we show that if the Chern scalar curvature is uniformly bounded for all time, then the flow converges smoothly to the unique Chern–Ricci-flat metric in almost Hermitian geometry.