Related papers: Lee classes on LCK manifolds with potential

We investigate the relation between holomorphic torus actions on complex manifolds of LCK type and the existence of special LCK metrics. We show that if the group of biholomorphisms of such a manifold $(M,J)$ contains a non-real compact…

We study Lie group structures on groups of the form C^\infty(M,K)}, where M is a non-compact smooth manifold and K is a, possibly infinite-dimensional, Lie group. First we prove that there is at most one Lie group structure with Lie algebra…

We show that for a certain class of solvable Lie groups, if they admit a left-invariant non-Vaisman locally conformally K\"{a}hler metric and a lattice, they must arise from the construction of Oeljeklaus-Toma manifolds. This result…

Let $M$ be an irreducible holomorphically symplectic manifold. We show that all faces of the Kahler cone of $M$ are hyperplanes $H_i$ orthogonal to certain homology classes, called monodromy birationally minimal (MBM) classes. Moreover, the…

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…

In this paper, we study a special type of compact Hermitian manifolds that are Strominger K\"ahler-like, or SKL for short. This condition means that the Strominger connection (also known as Bismut connection) is K\"ahler-like, in the sense…

The exterior derivative $d \theta$ of the Lee form $\theta$ of almost Hermitian manifolds is studied. If $\omega$ is the K\"ahler two-form, it is proved that the $\mathbb{R}\omega$-component of $d\theta$ is always zero. expressions for the…

We investigate a new property for compact Kahler manifolds. Let X be a Kahler manifold of dimension n and let H^{1,1} denote the (1,1) part of its real second cohomology. On this space, we have an degree n form given by cup product. Let K…

Compact K\"ahler manifolds classically satisfy the Hard Lefschetz Theorem, which gives strong control on the underlying topology of the manifold. One expects a similar theorem to be true for K\"ahler Lie Algebroids, and we show for a…

Let $(X,\omega)$ be a compact Hermitian manifold of complex dimension $n$. In this article, we first survey recent progress towards Grauert-Riemenschneider type criterions. Secondly, we give a simplified proof of Boucksom's conjecture given…

Inspired by the work of Z. Lu and G. Tian [8], A. Loi, F. Salis and F. Zuddas address in [5] the problem of studying those K\"ahler manifolds satisfying the $\Delta$-property, i.e. such that on a neighborhood of each of its points the…

On an almost complex manifold $(M,J)$, a pluricanonical locally conformally almost K\"ahler (LCAK) metric $g$ is induced by a locally conformally symplectic structure $(F,\theta)$ of the first kind, characterized by the fact that $D\theta$…

This article reveals a significant connection in geometry: when the Lee form $\theta$ is normal to an almost Hermitian manifold $N$, it implies that $N$ possesses a nearly K\"ahler structure. Investigating locally conformally Spin(7)…

Let $M$ be a hyperkahler manifold of maximal holonomy (that is, an IHS manifold), and let $K$ be its Kahler cone, which is an open, convex subset in the space $H^{1,1}(M, R)$ of real (1,1)-forms. This space is equipped with a canonical…

A rigid cohomology class on a complex manifold is a class that is represented by a unique closed positive current. The positive current representing a rigid class is also called rigid. For a compact Kahler manifold $X$ all eigenvectors of…

A compact symplectic manifold $(M, \omega)$ is said to satisfy the hard-Lefschetz condition if it is possible to develop an analogue of Hodge theory for $(M, \omega)$. This loosely means that there is a notion of harmonicity of differential…

Fr\"olicher spaces form a cartesian closed category which contains the category of smooth manifolds as a full subcategory. Therefore, mapping groups such as C^\infty(M,G) or \Diff(M), but also projective limits of Lie groups are in a…

We first give a deformation theory of integrable distributions of codimension 1. We define a parametrization of families of smooth hypersurfaces near a Levi flat hypersurface L such that the Levi flat deformations are given by the solutions…

We define a complex whose cohomology group of order 1 contains the infinitesimal deformations of a Levi flat structure on a smooth manifold. In the case of real analytic Levi flat structures, this cohomology group is the product of the…

A cohomogeneity one manifold is a manifold with the action of a compact Lie group, whose quotient is one dimensional. Such manifolds are of interest in Riemannian geometry, in the context of nonnegative sectional curvature, as well as in…