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arXiv · 2606.23540

Long-time existence of the pluriclosed flow on some fibrations

Elia Fusi·James Stanfield·Luigi Vezzoni
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Abstract

We prove long-time existence of the pluriclosed flow on certain compact quotients of Lie groups for non-invariant initial data, as well as on some holomorphic principal torus bundles over nonpositively curved K\"ahler manifolds. In particular, our results cover the cases of nilmanifolds and almost-abelian solvmanifolds, and provide a new proof of the long-time existence of the pluriclosed flow on certain complex surfaces, originally established by Garcia-Fernandez, Jordan, and Streets. These results follow from a general theorem on holomorphic submersions, which is of independent interest and, in particular, also implies the long-time existence of the pluriclosed flow on Oeljeklaus-Toma manifolds, as proved by Streets and Wang.

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Elia Fusi, James Stanfield, Luigi Vezzoni. 2026-06-22. Long-time existence of the pluriclosed flow on some fibrations. https://arxiv.org/abs/2606.23540

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