We study the quaternionic Calabi-Yau problem in HyperKähler manifolds with torsion geometry, introduced by Alesker and Verbitsky in [5], on eight-dimensional two-step nilmanifolds $M$ with an Abelian hypercomplex structure. We show that on these manifolds the quaternionic Monge-Ampère equation can always be solved for any data that are invariant under the action of a three-Torus.
The quaternionic Calabi Conjecture on abelian Hypercomplex Nilmanifolds Viewed as Tori Fibrations
Giovanni Gentili;Luigi Vezzoni
2022-01-01
Abstract
We study the quaternionic Calabi-Yau problem in HyperKähler manifolds with torsion geometry, introduced by Alesker and Verbitsky in [5], on eight-dimensional two-step nilmanifolds $M$ with an Abelian hypercomplex structure. We show that on these manifolds the quaternionic Monge-Ampère equation can always be solved for any data that are invariant under the action of a three-Torus.
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