Related papers: A characterization of compact locally conformally …
A locally conformally K\"ahler (LCK) manifold is a complex manifold covered by a K\"ahler manifold, with the covering group acting by homotheties. We show that if such a compact manifold X admits a holomorphic submersion with positive…
We characterize compact locally conformally K\"ahler (l.c.K.) manifolds under the assumption of a purely conformal, holomorphic circle action. As an application, we determine the structure of the compact l.c.K. manifolds with parallel Lee…
We present an overview of recent results in locally conformally K\"ahler geometry, with focus on the topological properties which obstruct the existence of such structures on compact manifolds.
A locally conformally K\"ahler (lcK) manifold is a complex manifold $(M,J)$ together with a Hermitian metric $g$ which is conformal to a K\"ahler metric in the neighbourhood of each point. In this paper we obtain three classification…
A locally conformally Kahler (LCK) manifold is a complex manifold admitting a Kahler covering M, such that its monodromy acts on this covering by homotheties. A compact LCK manifold is called LCK with potential if M admits an authomorphic…
A locally conformally K\"ahler (LCK) manifold $M$ is one which is covered by a K\"ahler manifold $\tilde M$ with the deck transform group acting conformally on $\tilde M$. If $M$ admits a holomorphic flow, acting on $\tilde M$ conformally,…
A locally conformally K\"ahler (LCK) manifold is a complex manifold $M$ which has a K\"ahler structure on its cover, such that the deck transform group acts on it by homotheties. Assume that the K\"ahler form is exact on the minimal…
A manifold $M$ is locally conformally Kahler (LCK) if it admits a Kahler covering with monodromy acting by holomorphic homotheties. Let $M$ be an LCK manifold admitting a holomorphic conformal flow of diffeomorphisms, lifted to a…
A Hopf manifold is a compact complex manifold of which the universal covering is C^n\{0}. In this note we show that any Hopf manifold admits a locally conformally Kaehler structure (shortly lcK structure), by constructing a complex analytic…
We study complex non-K\"ahler manifolds with Hermitian metrics being locally conformal to metrics with special cohomological properties. In particular, we provide examples where the existence of locally conformal holomorphic-tamed…
We obtain an example of a compact locally conformal symplectic nilmanifold which admits no locally conformal K\"ahler metrics. This gives a new positive answer to a question raised by L. Ornea and M. Verbitsky.
We show that a compact Kahler manifold admitting a nondegenerate holomorphic 2-form valued in a line bundle is a finite cyclic cover of a hyperkahler manifold. With respect to the connection induced by the locally hyperkahler metric, the…
We prove that a compact toric locally conformally K\"ahler manifold which is not K\"ahler admits a toric Vaisman structure, a fact which was conjectured in \cite{mmp}. This is the final step leading to the classification of compact toric…
We prove various classification results for homogeneous locally conformally symplectic manifolds. In particular, we show that a homogeneous locally conformally Kaehler manifold of a reductive group is of Vaisman type, if the normalizer of…
We give a short proof of the fact that compact pluricanonical locally conformally K\"ahler manifolds have parallel Lee form.
A manifold M is locally conformally Kahler (LCK) if it admits a Kahler covering with monodromy acting by holomorphic homotheties. For a compact connected group G acting on an LCK manifold by holomorphic automorphisms, an averaging procedure…
We propose an approach to the existence problem for locally conformally K\"ahler metrics on compact complex manifolds by introducing and studying a functional that is different according to whether the complex dimension of the manifold is…
We consider several transformation groups of a locally conformally K\"ahler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally…
An LCK (locally conformally Kahler) manifold is a complex manifold admitting a Kahler covering with monodromy acting by homotheties. Hopf manifolds and their submanifolds are the prime examples. This book presents an introduction to the…
In this thesis, we study cohomological properties of non-K\"ahler manifolds. In particular, we are concerned in investigating the cohomology of compact (almost-)complex manifolds, and of manifolds endowed with special structures, e.g.,…