We apply the quaternionic Jordan form to classify the nilpotent hypercomplex almost abelian
Lie algebras in all dimensions and to carry out the complete classification of 12-dimensional …

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Motivated by the construction based on topological suspension of a family of compact non-
K\" ahler complex manifolds with trivial canonical bundle given by L. Qin and B. Wang in …

We consider the natural generalization of the parabolic Monge–Ampère equation to HKT
geometry. We prove that in the compact case the equation has always a short-time solution …

We study complex solvmanifolds Γ\G with holomorphically trivial canonical bundle. We show
that the trivializing section of this bundle can be either invariant or non-invariant by the …

Mainly motivated by a conjecture of Alesker and Verbitsky, we study a class of fully non-
linear elliptic equations on certain compact hyperhermitian manifolds. By adapting the …

We give a characterization of almost abelian Lie groups carrying left invariant hypercomplex
structures and we show that the corresponding Obata connection is always flat. We …

Pursuing the approach of Gentili and Vezzoni [Math. Res. Not. IMRN 12 (2022), pp. 9499–
9528] we study the quaternionic Monge-Ampère equation on HKT (hyperkähler with torsion) …

We show that the parabolic quaternionic Monge–Ampère equation on a compact
hyperkähler manifold has always a long-time solution which, once normalized, converges …

Let be a compact HKT manifold, and let us denote with the conjugate Dolbeault operator
with respect to I,,, where Λ is the adjoint of. Under suitable assumptions, we study Hodge …