Related papers: A report on locally conformally K\"ahler manifolds

The K\"ahler cone of a compact manifold carries a natural Riemannian metric, given by the intersection product of its cohomology ring. We write down the curvature tensor of this metric by embedding the K\"ahler cone in the space of…

Locally conformally Kahler (LCK) manifolds with potential are those which admit a Kahler covering with a proper, automorphic Kaehler potential. Existence of a potential can be characterized cohomologically as a vanishing of a certain…

Motivated by understanding the limiting case of a certain systolic inequality we study compact Riemannian manifolds having all harmonic 1-forms of constant length. We give complete characterizations as far as K\"ahler and hyperbolic…

The property of admitting an astheno-K\"ahler metric is not stable under the action of small deformations of the complex structure of a compact complex manifold. In this paper, we prove necessary cohomological conditions for the existence…

The aim of this paper is to classify compact Kahler manifolds with quasi-constant holomorphic sectional curvature.

The aim of this paper is to classify compact, simply connected K\"ahler manifolds which admit totally geodesic, holomorphic complex homothetic foliation by curves.

We prove that any compact homogeneous locally conformally K\"ahler manifold has parallel Lee form.

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…

Let $M^{2n}$ be a compact Riemannian manifold of non-positive (resp. negative) sectional curvature. We call $(M,J,\theta)$ a $d$(bounded) locally conformally K\"{a}hler manifold if the lifted Lee form $\tilde{\theta}$ on the universal…

We prove the hard Lefschetz duality for locally conformally almost K\"{a}hler manifolds. This is a generalization of that for almost K\"{a}hler manifolds studied by Cirici and Wilson. We generalize the K\"{a}hler identities to prove the…

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…

The structure of nearly K\"ahler manifolds was studied by Gray in several papers. More recently, a relevant progress on the subject has been done by Nagy. Among other results, he proved that a strict and complete nearly K\"ahler manifold is…

We prove that any holomorphic geometric structure of affine type on an Oeljeklaus- Toma manifold is locally homogeneous. For locally conformal K\"ahler Oeljeklaus-Toma manifolds we prove that all holomorphic geometric structures, and also…

We give a complex polarized variation of Hodge structure over a compact K"ahler manifold $M$ which controls all finite-dimensional complex polarized variations of Hodge structure over $M$ and their tensor relations. As a corollary, we…

We show a bijective correspondence between compact toric locally conformally symplectic manifolds which admit a compatible complex structure and pairs $(C,a)$, where $C$ is a good cone in the dual Lie algebra of the torus and $a$ is a…

In this paper, we build a compactification by a strictly pseudoconvex CR structure for complete and non-compact K\"ahler manifolds whose curvature tensor is asymptotic to that of the complex hyperbolic space.

We consider compatibility conditions between Poisson and Riemannian structures on smooth manifolds by means of a contravariant partially complex structure, or $f$-structure, introducing the notion of (almost) K\"ahler--Poisson manifolds. In…

We prove the existence of canonical tubular neighbourhoods around complex submanifolds of K\"ahler manifolds that are adapted to both the holomorphic and symplectic structure. This is done by solving the complex Homogeneous Monge-Amp\`ere…

We show the existence of a compact K\"ahler manifold which does not fit in a proper flat family over an irreducible base with one projective (possibly singular) fiber. We also give a topological version of this statement. This strengthens…

The object of the present paper is to study some properties of para-K$\"{a}$hler manifold whose metric is conformal Einstein soliton. We have studied some certain curvature properties of para-K$\"{a}$hler manifold admitting conformal…