8 papers · 1 filter
On products of locally conformally Kähler manifolds
Miron Stanciu
We prove that no product of positive-dimensional compact complex manifolds admits a strict locally conformally Kähler (lcK) metric. This solves a long-standing conjecture in lcK ge…
Dolbeault cohomology of Endo-Pajitnov manifolds
Liviu Ornea, Miron Stanciu
Endo-Pajitnov manifolds are compact non-Kähler manifolds which generalize the Inoue surfaces to higher dimensions. We compute their Dolbeault cohomology and show that they sa…
Special non-Kähler metrics -- old and new
Liviu Ornea, Miron Stanciu
We give an account of old and new results concerning many types of non-Kähler metrics, with focus on the problem of their coexistence on compact complex manifolds, and their behavi…
Vaisman's theorem and local reducibility
Ovidiu Preda, Miron Stanciu
As proven in a celebrated theorem due to Vaisman, pure locally conformally Kähler metrics do not exist on compact Kähler manifolds. In a previous paper, we extended this result to…
Special non-Kähler metrics on Endo-Pajitnov manifolds
Cristian Ciulică, Alexandra Otiman, Miron Stanciu
We investigate the metric and cohomological properties of higher dimensional analogues of Inoue surfaces, that were introduced by Endo and Pajitnov. We provide a solvmanifold struc…
Blow-ups and modifications of lcK spaces
Ovidiu Preda, Miron Stanciu
In this article, we prove that the blow-up of a locally irreducible lcK space along a subspace which verifies certain conditions is lcK if and only if is induced gcK, g…