Related papers: Holomorphically parallelizable solvmanifolds with …

We establish the existence of complete K\"ahler metrics of semi-positive holomorphic sectional curvature with many zeroes in an interesting and natural geometric setting. Specifically, we use Calabi's Ansatz in the form due to Koiso-Sakane…

A torsion-free G_2 structure admitting an infinitesimal isometry is shown to give rise to a 4-manifold equipped with a complex symplectic structure and a 1-parameter family of functions and 2-forms linked by second order equations.…

The aim of this paper is to construct left-invariant Einstein pseudo-Riemannian Sasaki metrics on solvable Lie groups. We consider the class of $\mathfrak z$-standard Sasaki solvable Lie algebras of dimension $2n+3$, which are in one-to-one…

LVMB manifolds are a class of non-K\"ahler compact complex manifolds with a remarkably rich geometry: in many cases they admit a holomorphic bundle structure over a compact toric manifold. In fact, such a bundle is determined by an…

In this paper, we consider the problem of existence and multiplicity of conformal metrics on a riemannian compact $4-$dimensional manifold $(M^4,g_0)$ with positive scalar curvature. We prove new exitence criterium which provides existence…

We review the relations between compact complex manifolds carrying various types of Hermitian metrics (K\"ahler, balanced or {\it strongly Gauduchon}) and those satisfying the $\partial\bar\partial$-lemma or the degeneration at $E_1$ of the…

The Hitchin-Kobayashi correspondence for vector bundles, established by Donaldson, Kobayashi, Luebke, Uhlenbeck and Yau, states that an indecomposable holomorphic vector bundle over a compact Kaehler manifold is stable in the sense of…

Given a complete K\"ahler manifold $(X,\,\omega)$ with finite second Betti number, a smooth complex hypersurface $Y\subset X$ and a smooth real $d$-closed $(1,\,1)$-form $\alpha$ on $X$ with arbitrary, possibly non-rational, De Rham…

On a compact K\"ahler manifold, we introduce a notion of almost nonpositivity for the holomorphic sectional curvature, which by definition is weaker than the existence of a K\"ahler metric with semi-negative holomorphic sectional curvature.…

Using Seiberg-Witten theory, it is shown that any Kaehler metric of constant negative scalar curvature on a compact 4-manifold M minimizes the L^2-norm of scalar curvature among Riemannian metrics compatible with a fixed decomposition…

Given a compact K\"ahler manifold $X$ it is interesting to ask whether it admits a constant scalar curvature K\"ahler (cscK) metric. In this short note we show that there always exist cscK metrics on compact K\"ahler manifolds with nef…

We give an explicit formula for the quaternionic K\"ahler metrics obtained by the HK/QK correspondence. As an application, we give a new proof of the fact that the Ferrara-Sabharwal metric as well as its one-loop deformation is quaternionic…

We investigate stability conditions related to the existence of solutions of the Hull-Strominger system with prescribed balanced class. We build on recent work by the authors, where the Hull-Strominger system is recasted using non-Hermitian…

Given a semi-Riemannian $4$-manifold $(M,g)$ with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of K\"ahler metrics $g_K$ is constructed, defined on an…

We prove the instability of some families of Riemannian manifolds with non-trivial real Killing spinors. These include the invariant Einstein metrics on the Aloff-Wallach spaces $N_{k, l}={\rm SU}(3)/i_{k, l}(S^{1})$ (which are all nearly…

We consider an almost complex manifold with Norden metric (i. e. a metric with respect to which the almost complex structure is an anti-isometry). On such a manifold we study a linear connection preserving the almost complex structure and…

We extend the Abreu-Guillemin theory of invariant K\"ahler metrics from toric symplectic manifolds to any symplectic manifold admitting a toric action of a symplectic torus bundle. We show that these are precisely the symplectic manifolds…

Let $D$ be a smooth divisor in a compact complex manifold $X$ and let $\beta \in (0,1)$. We show that in any positive co-homology class on $X$ there is a K\"ahler metric with cone angle $2\pi\beta$ along $D$ which has bounded Ricci…

Suppose that a polarised K\"ahler manifold $(X,L)$ admits an extremal metric $\omega$. We prove that there exists a sequence of K\"ahler metrics $\{ \omega_k \}_k$, converging to $\omega$ as $k \to \infty$, each of which satisfies the…

We continue our study on Hermitian manifolds that are {\em Bismut torsion parallel,} or {\em BTP} for brevity, which means that the Bismut connection has parallel torsion tensor. For $n\geq 3$, BTP metrics can be balanced (and…