The quaternionic Calabi conjecture on abelian hypercomplex nilmanifolds viewed as tori fibrations
Differential Geometry
2021-01-07 v2
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.
Keywords
Cite
@article{arxiv.2006.05773,
title = {The quaternionic Calabi conjecture on abelian hypercomplex nilmanifolds viewed as tori fibrations},
author = {Giovanni Gentili and Luigi Vezzoni},
journal= {arXiv preprint arXiv:2006.05773},
year = {2021}
}
Comments
20 pages, to appear in IMRN