Quaternionic Bott-Chern cohomology and existence of HKT metrics

TL;DR

This paper explores quaternionic Bott-Chern cohomology on compact hypercomplex manifolds, establishing criteria for the existence of HKT metrics in eight-dimensional cases by adapting complex geometric methods.

Contribution

It introduces quaternionic Bott-Chern cohomology and provides a new criterion for HKT metric existence on compact hypercomplex manifolds of dimension 8.

Findings

Established a criterion for HKT metrics on 8-dimensional hypercomplex manifolds.

Adapted complex geometric results to the quaternionic setting.

Extended understanding of cohomological conditions for special metrics.

Abstract

We study quaternionic Bott-Chern cohomology on compact hypercomplex manifolds and adapt some results from complex geometry to the quaternionic setting. For instance, we prove a criterion for the existence of HKT metrics on compact hypercomplex manifolds of real dimension 8 analogous to the one given by Teleman [35] and Angella-Dloussky-Tomassini [3] for compact complex surfaces.