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

We give several characterizations of relative homological epimorphisms in the setting of locally convex topological algebras, thereby correcting a gap in our earlier paper [Trans. Moscow Math. Soc. 2008, 27-104].

We present some fundamental facts about a class of generalized K\"ahler structures defined by invariant complex structures on compact Lie groups. The main computational tool is the BH-to-GK spectral sequences that relate the bi-Hermitian…

The existence of orthogonal local coordinates is a generalization of the manifold being conformally flat. It is always possible to construct orthogonal coordinates on 2-manifolds, using geometric normal coordinates or isothermal…

We study the interplay between the following types of special non-K\"ahler Hermitian metrics on compact complex manifolds: it locally conformally K\"ahler, $k$-Gauduchon, balanced and locally conformally balanced and prove that a locally…

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…

We investigate the existence of $p$-K\"ahler structures on two classes of complex manifolds: on quasi-regular fibrations, with particular emphasis on complex homogeneous spaces, and on reductive Lie groups endowed with invariant complex…

In this note, we show that the obstruction classes of deforming vector forms on a compact K\"ahler manifold is annihilated by cohomology classes.

This paper is devoted to a general and self-contained approach to any cohomological field theory with K\"{a}hler structure.

We revisit Brunella's proof of the fact that Kato surfaces admit locally conformally K\" ahler metrics, and we show that it holds for a large class of higher dimensional complex manifolds containing a global spherical shell. On the other…

On a K\"ahler manifold we consider the problems of maximizing/minimizing Monge--Amp\`ere energy over certain subsets of the space of K\"ahler potentials. Under suitable assumptions we prove that solutions to these variational problems…

The coadjoint orbits of compact Lie groups each carry a canonical (positive definite) K\"ahler structure, famously used to realize the group's irreducible representations in holomorphic sections of appropriate line bundles (Borel-Weil…

Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant complex structure J and compatible metric g, which is not required to be invariant. We give classifications of 6-dimensional nilmanifolds M admitting strong…

The aim of this paper is to introduce and give preliminary investigation of T-locally compact spaces. Locally compact and T-locally compact are independent of each other. Every Hausdorff, locally compact space is T-locally compact.…

By the work of Li, a compact co-K\"ahler manifold $M$ is a mapping torus $K_\varphi$, where $K$ is a K\"ahler manifold and $\varphi$ is a Hermitian isometry. We show here that there is always a finite cyclic cover $\bar M$ of the form $\bar…

In a preceding paper we introduced a notion of compatibility between a Jacobi structure and a Riemannian structure on a smooth manifold. We proved that in the case of fundamental examples of Jacobi structures : Poisson structures, contact…

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…

We obtain a class of locally symmetric Kaehler Einstein structures on the cotangent bundle of a Riemannian manifold of negative sectional curvature. Similar results are obtained in the case of a Riemannian manifold of positive sectional…

We characterize compact locally conformal parallel $G_2$ (respectively, $Spin(7)$) manifolds as fiber bundles over $S^1$ with compact nearly K\"ahler (respectively, compact nearly parallel $G_2$) fiber. A more specific characterization is…

In this paper, we establish new Laplacian comparison theorems and rigidity theorems for complete K\"ahler manifolds under new curvature notions that interpolate between Ricci curvature and holomorphic bisectional curvature.

We study restrictions on cohomology algebras of Kaehler compact manifolds, not depending on the h^{p,q} numbers or the symplectic structure. To illustrate the effectiveness of these restrictions, we give a number of examples of compact…