English

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