Related papers: Bimeromorphic geometry of LCK manifolds

Let $M$ be a real $l$-dimensional minimal submanifold with flat normal connection in a kaehler product manifold $\overline{M}^m\times \overline{M}^n$ where $\overline{M}^m$ and $\overline{M}^n$ are complex $m$-dimensional and complex…

We classify and investigate locally conformally K\"ahler structures on four-dimensional solvable Lie algebras up to linear equivalence. As an application we can produce many examples in higher dimension, here including lcK structures on…

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…

Let $(M^n, g)$ be a complete non-compact K\"ahler manifold with non-negative and bounded holomorphic bisectional curvature. We prove that $M$ is holomorphically covered by a pseudoconvex domain in $\C^n$ which is homeomorphic to $\R^{2n}$,…

We study the J-invariant and J-anti-invariant cohomological subgroups of the de Rham cohomology of a compact manifold M endowed with an almost-K\"ahler structure (J, \omega, g). In particular, almost-K\"ahler manifolds satisfying a…

In this article, we study harmonic symmetries on the compact locally conformally K\"{a}hler manifold $M$ of $dim_{\mathbb{C}}=n$. The space of harmonic symmetries is a subspace of harmonic differential forms which defined by the kernel of a…

We consider compact K\"ahler manifolds acted on by a connected compact Lie group $K$ of isometries in Hamiltonian fashion. We prove that the squared moment map $\|\mu\|^2$ is constant if and only if the manifold is biholomorphically and…

We study the exceptional loci of birational (bimeromorphic) contractions of a hyperk\"ahler manifold $M$. Such a contraction locus is the union of all minimal rational curves in a collection of cohomology classes which are orthogonal to a…

A Hopf manifold is a quotient of $C^n\backslash 0$ by the cyclic group generated by a holomorphic contraction. Hopf manifolds are diffeomorphic to $S^1\times S^{2n-1}$ and hence do not admit Kahler metrics. It is known that Hopf manifolds…

Using examples of compact complex 3-manifolds which arise as twistor spaces, we show that the class of compact complex manifolds bimeromorphic to K\"ahler manifolds is not stable under small deformations of complex structure.

In this paper, we study the complex structures of complete hyperk\"ahler four-manifolds of infinite topological type arising from the Gibbons-Hawking ansatz. We show that for almost all complex structures in the hyperk\"ahler family, the…

The aim of this paper is to present the first examples of compact, simply connected holomorphically pseudosymmetric Kahler manifolds.

This is partly a survey and partly a research article. Some known results and open problems about Kaehler groups (fundamental groups of compact Kaehler manifolds) are discussed. A new notion of Kaehler homomorphism is introduced. This is a…

In this paper, we construct metallic K\"ahler and nearly metallic K\"ahler structures on Riemanian manifolds. For such manifolds with these structures, we study curvature properties. Also we describe linear connections on the manifold,…

We prove that locally conformally K\"ahler metrics on certain compact complex surfaces with odd first Betti number can be deformed to new examples of bi-Hermitian metrics.

We consider locally conformal Kaehler geometry as an equivariant, homothetic Kaehler geometry (K,\Gamma). We show that the de Rham class of the Lee form can be naturally identified with the homomorphism projecting \Gamma to its dilation…

In this paper, we prove a stability result for the non-K\"ahler geometry of locally conformally K\"ahler (lcK) spaces with singularities. Specifically, we find sufficient conditions under which the image of an lcK space by a holomorphic…

We survey recent developments which led to the proof of the Benson-Gordon conjecture on K\"ahler quotients of solvable Lie groups. In addition we prove that the Albanese morphism of a K\"ahler manifold which is a homotopy torus is a…

We show that a compact K\"ahler manifold bimeromorphic to a weakly K\"ahler hyperbolic manifold is weakly K\"ahler hyperbolic, providing an answer to a problem raised by J. Koll\'ar in his 1995 book "Shafarevic maps and automorphic forms"

In this short note, using Siu-Yau's method [14], we give a new proof that any n-dimensional compact Kahler manifold with positive orthogonal bisectional curvature must be biholomorphic to $\mathbb{P}^n$.