On the Calabi flow on quasi-Kähler manifolds

Masaya Kawamura ()
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Masaya Kawamura: Sugiyama Jogakuen University

Partial Differential Equations and Applications, 2026, vol. 7, issue 1, 1-32

Abstract: Abstract 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.

Keywords: Calabi flow; Quasi-Kähler manifold; Chern connection; Primary 32Q60; Secondary 53C15; 53C55 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s42985-025-00363-w

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