3 papers
math.DG2026
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…
math.DG2026
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…
math.DG2025
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…