13 citations · 71 across the 15 of their papers we have counts for
18 papers
Locally Conformally Kähler Manifolds of Algebraic Codimension One
Liviu Ornea, Misha Verbitsky, Victor Vuletescu
A locally conformally Kähler (LCK) manifold is a manifold which admits a Kähler structure on its universal cover , in such a way that the monodromy acts conformally o…
Do products of compact complex manifolds admit LCK metrics?
Liviu Ornea, Misha Verbitsky, Victor Vuletescu
An LCK (locally conformally Kahler) manifold is a Hermitian manifold which admits a Kahler cover with deck group acting by holomorphic homotheties with respect to the Kahler metric…
On Locally Conformally K\" ahler metrics on Oeljeklaus-Toma Manifolds
Stefan Deaconu, Victor Vuletescu
We show that Oeljeklaus-Toma manifolds where is a number field of signature such that and admit no lck metric. Combined with…
On locally conformally Kähler threefolds with algebraic dimension two
Daniele Angella, Maurizio Parton, Victor Vuletescu
The paper is part of an attempt of understanding non-Kähler threefolds. We start by looking at compact complex non-Kähler threefolds with algebraic dimension two and admitting loca…
Classification of non-Kahler surfaces and locally conformally Kahler geometry
Liviu Ornea, Victor Vuletescu, Misha Verbitsky
We give a mostly self-contained proof of the classification of non-Kahler surfaces based on Buchdahl-Lamari theorem. We also prove that all non-Kahler surfaces which are not of cla…
Automorphisms of OT manifolds and ray class numbers
Oliver Braunling, Victor Vuletescu
We compute the automorphism group of OT manifolds of simple type. We show that the graded pieces under a natural filtration are related to a certain ray class group of the underlyi…
Flat affine subvarieties in Oeljeklaus-Toma manifolds
Liviu Ornea, Misha Verbitsky, Victor Vuletescu
The Oeljeklaus-Toma (OT-) manifolds are compact, complex, non-Kahler manifolds constructed by Oeljeklaus and Toma, and generalizing the Inoue surfaces. Their construction uses the…
Rigidity of Oeljeklaus-Toma manifolds
Daniele Angella, Maurizio Parton, Victor Vuletescu
We prove that Oeljeklaus-Toma manifolds of simple type are rigid, and that any line bundle on an Oeljeklaus-Toma manifold is flat.
Clifford systems in octonionic geometry
Maurizio Parton, Paolo Piccinni, Victor Vuletescu
We give an inductive construction for irreducible Clifford systems on Euclidean vector spaces. We then discuss how this notion can be adapted to Riemannian manifolds, and outline s…
Weighted Bott-Chern and Dolbeault cohomology for LCK-manifolds with potential
Liviu Ornea, Misha Verbitsky, Victor Vuletescu
A locally conformally Kahler (LCK) manifold is a complex manifold with a Kahler structure on its covering and the deck transform group acting on it by holomorphic homotheties. One…
LCK metrics on Oeljeklaus-Toma manifolds versus Kronecker's theorem
Victor Vuletescu
A locally conformally Kähler (LCK) manifold is a manifold which is covered by a Kähler manifold, with the deck transform group acting by homotheties. We show that the search for LC…
A restriction theorem for torsion-free sheaves on some elliptic manifolds
Victor Vuletescu
We prove that if is the total space of an elliptic principal bundle $π:X\ra B$ which is non-Kähler, then the restriction of any torsion-free sheaf on to the general fiber o…
Spin(9) geometry of the octonionic Hopf fibration
Liviu Ornea, Maurizio Parton, Paolo Piccinni +1
We deal with Riemannian properties of the octonionic Hopf fibration S^{15}-->S^8, in terms of the structure given by its symmetry group Spin(9). In particular, we show that any ver…
Holomorphic submersions of locally conformally Kähler manifolds
Liviu Ornea, Maurizio Parton, Victor Vuletescu
A locally conformally Kähler (LCK) manifold is a complex manifold covered by a Kähler manifold, with the covering group acting by homotheties. We show that if such a compact manifo…
Blow-ups of locally conformally Kahler manifolds
Liviu Ornea, Misha Verbitsky, Victor Vuletescu
A locally conformally Kahler (LCK) manifold is a manifold which is covered by a Kahler manifold, with the deck transform group acting by homotheties. We show that the blow-up of a…
Examples of non-trivial rank in locally conformal Kähler geometry
Maurizio Parton, Victor Vuletescu
We consider locally conformal Kaehler geometry as an equivariant, homothetic Kaehler geometry (K,Γ). We show that the de Rham class of the Lee form can be naturally identified with…
LCK metrics on elliptic principal bundles
Victor Vuletescu
For elliptic principal bundles $π:X\ra B$ over Kähler manifolds it was shown by Blanchard that has a Kähler metric if and only both Chern classes (with real coefficients) of $π…
Blowing-up points on l.c. K. manifolds
Victor Vuletescu
It is a classical result, due to F. Tricceri, that the blow-up of a manifold of locally conformally Kähler (l.c.K. for short) type at some point is again of l.c.K. type. However, t…