The quaternionic Calabi Conjecture on abelian Hypercomplex Nilmanifolds Viewed as Tori Fibrations-Reference-Cited by-同舟云学术

The quaternionic Calabi Conjecture on abelian Hypercomplex Nilmanifolds Viewed as Tori Fibrations

Published:2021-03-22 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Gentili Giovanni¹,Vezzoni Luigi¹

Affiliation:

1. Dipartimento di Matematica G. Peano, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy

Abstract

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.

Funder

Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni

Istituto Nazionale di Alta Matematica

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnab004/36646623/rnab004.pdf

Reference28 articles.

1. Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables;Alesker;Bull. Sci. Math.,2003

2. Solvability of the quaternionic Monge-Ampère equation on compact manifolds with a flat hyperKähler metric;Alesker;Adv. Math.,2013

3. A uniform estimate for general quaternionic Calabi problem (with appendix by Daniel Barlet);Alesker;Adv. Math.,2017

4. Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry;Alesker;J. Glob. Anal.,2006

5. Quaternionic Monge-Ampère equations and Calabi problem for HKT-manifolds;Alekser;Israel J. Math.,2010

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Octonionic Calabi–Yau Theorem;The Journal of Geometric Analysis;2024-07-10

2. The Monge–Ampère equation for $$(n-1)$$-quaternionic PSH functions on a hyperKähler manifold;Mathematische Zeitschrift;2024-05-10

3. HKT Manifolds: Hodge Theory, Formality and Balanced Metrics;The Quarterly Journal of Mathematics;2024-04-04

4. On the Alesker-Verbitsky Conjecture on HyperKähler Manifolds;Geometric and Functional Analysis;2023-06-20

5. Solvability of a class of fully nonlinear elliptic equations on tori;Annali di Matematica Pura ed Applicata (1923 -);2023-05-31