Quaternionic Bott-Chern cohomology and existence of HKT 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.