The quaternionic Calabi conjecture on abelian hypercomplex nilmanifolds viewed as tori fibrations
arXiv:2006.05773
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-Ampère equation on these manifolds can always be solved for every data which is invariant by the action of a 3-dimensional torus.
20 pages, to appear in IMRN