Miron Stanciu

activity

20152026

collaborators

13 papers

math.DG2026

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…

math.DG2026

Dolbeault cohomology of Endo-Pajitnov manifolds

Liviu Ornea, Miron Stanciu

Endo-Pajitnov manifolds are compact non-Kähler manifolds which generalize the Inoue surfaces $S_{M}$ to higher dimensions. We compute their Dolbeault cohomology and show that they sa…

math.DG2025

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…

math.DG2024

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…

math.DG2024

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…

math.CV2023

Locally conformally Kähler spaces and proper open morphisms

Ovidiu Preda, Miron Stanciu

In this paper, we prove a stability result for the non-Kähler geometry of locally conformally Kähler (lcK) spaces with singularities. Specifically, we find sufficient conditions un…

math.DG2022

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 $X$ along a subspace $Z$ which verifies certain conditions is lcK if and only if $X$ is induced gcK, g…

math.DG2021

Vaisman theorem for lcK spaces

Ovidiu Preda, Miron Stanciu

Vaisman's theorem for locally conformally Kähler (lcK) compact manifolds states that any lcK metric on a compact complex manifold which admits a Kähler metric is, in fact, globally…

math.DG2020

Compatibility between non-Kähler structures on complex (nil)manifolds

Liviu Ornea, Alexandra Otiman, Miron Stanciu

We study the interplay between the following types of special non-Kähler Hermitian metrics on compact complex manifolds: it locally conformally Kähler, $k$ -Gauduchon, balanced and…

math.DG2019

Coverings of locally conformally Kähler complex spaces

Ovidiu Preda, Miron Stanciu

In this paper, we study the properties of coverings of locally conformally Kähler (LCK) spaces with singularities. We begin by proving that a space is LCK if any only if its univer…

math.DG2019

Locally conformally symplectic reduction of the cotangent bundle

Miron Stanciu

In a previous article, we introduced a reduction procedure for locally conformally symplectic manifolds at any regular value of the momentum mapping. We use this construction to pr…

math.DG2018

Locally conformally symplectic reduction

Miron Stanciu

We present a reduction procedure for locally conformally symplectic (LCS) manifolds with an action of a Lie group preserving the conformal structure, with respect to any regular va…

math.DG2015

Darboux-Weinstein theorem for locally conformally symplectic manifolds

Alexandra Otiman, Miron Stanciu

A locally conformally symplectic (LCS) form is an almost symplectic form $ω$ such that a closed one-form $θ$ exists with $d ω = θ \land ω$ . We present a version of the well-known res…