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arXiv · 2006.05773

The quaternionic Calabi conjecture on abelian hypercomplex nilmanifolds viewed as tori fibrations

Giovanni Gentili·Luigi Vezzoni
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Abstract

We study the quaternionic Calabi-Yau problem in HKT geometry introduced by Alesker and Verbitsky on 8-dimensional 2-step nilmanifolds with an abelian hypercomplex structure. We show that the quaternionic Monge-Amp\`ere equation on these manifolds can always be solved for every data which is invariant by the action of a 3-dimensional torus.

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Giovanni Gentili, Luigi Vezzoni. 2020-06-10. The quaternionic Calabi conjecture on abelian hypercomplex nilmanifolds viewed as tori fibrations. https://arxiv.org/abs/2006.05773

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