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arXiv · 2610.07897

HKT geometry on locally conformally hyperkähler manifolds

Giovanni Gentili·Luigi Vezzoni
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Abstract

We study the HKT geometry of compact locally conformally hyperkähler manifolds. We prove that on these manifolds the quaternionic Monge-Ampère equation is always solvable, extending results of Alesker and of Dinew-Sroka, and we confirm the conjecture on the maximal existence time of the HKT-Ricci flow. On quaternionic Hopf surfaces we construct non-trivial HKT solitons and prove convergence of the normalized flow for symmetric initial data.

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Giovanni Gentili, Luigi Vezzoni. 2026-10-06. HKT geometry on locally conformally hyperkähler manifolds. https://arxiv.org/abs/2610.07897

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