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.

To appear in Quarterly Journal of Mathematics. Final version

References in corpus (6)

• On the $\partial \overline{\partial }$-Lemma and Bott-Chern cohomology
• Geometry of nilmanifolds with left-invariant complex structure and deformations in the large
• Inequalities à la Frölicher and cohomological decompositions
• On Bott-Chern cohomology of compact complex surfaces
• Existence of HKT metrics on hypercomplex manifolds of real dimension 8
• Cohomological aspects of non-Kähler manifolds