Hermitian curvature flow and HKT geometry

Beatrice Brienza; Jeffrey Streets

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arXiv · 2608.14358

Hermitian curvature flow and HKT geometry

Beatrice Brienza·Jeffrey Streets

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Abstract

We identify a Hermitian curvature flow which preserves HKT geometry, and whose fixed points are HKT-Einstein metrics, equivalent to a flow suggested by Verbitsky in the context of the quaternionic Monge-Ampère equation. We exhibit a fundamental regularity obstruction and a monotonicity formula for the Chern scalar curvature. We formulate a maximal existence time conjecture for this flow, and give a conditional resolution. We establish the existence conjecture in dimension four. We show the existence of a divergent sequence of HKT-Einstein metrics on quaternionic Hopf surfaces. These are the first non-homogeneous examples in the literature, and indicate the delicacy of the convergence question. Finally we classify which strong HKT structures arising from bi-invariant metrics on Lie groups are also HKT-Einstein.

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Beatrice Brienza, Jeffrey Streets. 2026-08-14. Hermitian curvature flow and HKT geometry. https://arxiv.org/abs/2608.14358

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