The quaternionic Calabi conjecture on abelian hypercomplex nilmanifolds viewed as tori fibrations (2006.05773v2)

Published 10 Jun 2020 in math.DG

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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