4 papers
A Levi-type decomposition on two-step solvable Lie algebras with a complex structure
Elia Fusi, Giovanni Gentili
We prove that a large class of -step solvable Lie algebras equipped with a complex structure admits a Levi-Malcev type decomposition, adapted to . As an application, we p…
Semi-integrable almost hyperhermitian structures
Giovanni Gentili, Andrei Moroianu
In this work, we introduce a family of almost hyperhermitian structures that we call semi-integrable. We subdivide them into four disjoint classes and show that each class is non-e…
Special metrics in hypercomplex geometry
Elia Fusi, Giovanni Gentili
We investigate the existence and geometric properties of special hyperhermitian metrics. First of all, we characterise hypercomplex structures with Obata holonomy in $\mathrm{SL}(n…
On balanced HKT manifolds
Giovanni Gentili, Mehdi Lejmi
We prove the openness of the balanced HKT cone within the cone of HKT structures on a compact hypercomplex manifold . We also study the Lie algebra of hyperholomorphic v…