Related papers: Locally conformally Kahler metrics obtained from p…

A locally conformally Kaehler (l.c.K.) manifold is a complex manifold admitting a Kaehler covering $\tilde M$, with each deck transformation acting by Kaehler homotheties. A compact l.c.K. manifold is Vaisman if it admits a holomorphic flow…

In this paper, we study the properties of coverings of locally conformally K\"ahler (LCK) spaces with singularities. We begin by proving that a space is LCK if any only if its universal cover is K\"ahler, thereby generalizing a result from…

We study two kinds of transformation groups of a compact locally conformally Kahler (l.c.K.) manifold. First we study compact l.c.K. manifolds with parallel Lee form by means of the existence of a holomorphic l.c.K. flow. Next, we introduce…

We give a complete description of all locally conformally K\"ahler structures with holomorphic Lee vector field on a compact complex manifold of Vaisman type. This provides in particular examples of such structures whose Lee vector field is…

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.

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…

The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the…

We prove that a compact lcK manifold with holomorphic Lee vector field is Vaisman provided that either the Lee field has constant norm or the metric is Gauduchon (i.e., the Lee field is divergence-free). We also give examples of compact lcK…

A locally conformally product (LCP) structure on compact manifold $M$ is a conformal structure $c$ together with a closed, non-exact and non-flat Weyl connection $D$ with reducible holonomy. Equivalently, an LCP structure on $M$ is defined…

We investigate isometric immersions of locally conformally Kaehler metrics into Hopf manifolds. In particular, we study Hopf-induced metrics on compact complex surfaces.

A locally conformally product (LCP) structure on a compact conformal manifold is a closed non-exact Weyl connection (i.e.~a linear connection which is locally but not globally the Levi-Civita connection of Riemannian metrics in the…

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 construct a Kahler structure (which we call a generalised Kahler cone) on an open subset of the cone of a strongly pseudo-convex CR manifold endowed with a 1-parameter family of compatible Sasaki structures. We determine those…

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 value of the momentum mapping. Under certain conditions, this…

We study compact locally conformally K\"ahler (lcK) manifolds which are Calabi--Yau, in the sense that $c_1^{BC}(X)=0$. First of all, we prove that all the known lcK manifolds which are Calabi--Yau are Vaisman. Then we prove that an lcK…

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 present some examples of locally conformal symplectic structures of the first kind on compact nilmanifolds which do not admit Vaisman metrics. One of these examples does not admit locally conformal K\"ahler metrics and all the structures…

We characterize the existence of a locally conformally K\"ahler metric on a compact complex manifold in terms of currents, adapting the celebrated result of Harvey and Lawson for K\"ahler metrics.

We show that every Kato surface (or surface with a global spherical shell) admits a locally conformally Kaehler metric.

We discuss a correspondence between certain contact pairs on the one hand, and certain locally conformally symplectic forms on the other. In particular, we characterize these structures through suspensions of contactomorphisms. If the…