arXiv research

The paper constructs a family of SKT metrics on the exceptional Lie group G2.

Stability of SKT metrics under deformations on complex manifolds.

Proves conjecture about compatible SKT and balanced metrics on compact solvmanifolds.

The study of invariant SKT structures on nilmanifolds, focusing on 2-step cases.

The paper defines two types of hyperbolicity for complex manifolds and proves related results.

The paper examines SKT and CYT metrics on Lie groups.

On a complex manifold an Hermitian metric which is simultaneously SKT and balanced has to be necessarily Kähler. It has been conjectured that if a compact complex manifold (M,J) has an SKT metric and a balanced metric both compatible with J, then (M, J) is necessarily Kähler. We show that the conjecture is true for nil…

A Hermitian metric on a complex manifold is called strong Kähler with torsion (SKT) if its fundamental 2-form $ω$ is $\partial \bar \partial$-closed. We review some properties of strong KT metrics also in relation with symplectic forms taming complex structures. Starting from a $2n$-dimensional SKT Lie algebra $\mathfr…

An SKT metric is a Hermitian metric on a complex manifold whose fundamental 2-form $ω$ satisfies $\de\debarω=0$. Streets and Tian introduced in \cite{sttiPlur} a Ricci-type flow that preserves the SKT condition. This flow uses the Ricci form associated to the Bismut connection, the unique Hermitian connection with tota…

The study explores polarized deformations of SKT Calabi-Yau manifolds using Aeppli classes.

Symplectic forms taming complex structures on compact manifolds are strictly related to Hermitian metrics having the fundamental form $\partial \bar \partial$-closed, i.e. to strong Kähler with torsion (${\rm SKT}$) metrics. It is still an open problem to exhibit a compact example of a complex manifold having a tamed …

Study SKT and CYT manifolds with parallel Bismut torsion.

Study geometric formal metrics and Massey products on Kähler manifolds with torsion.

New approach finds Kähler metrics on compact complex manifolds.

For an almost contact metric manifold $N$, we find conditions for which either the total space of an $S^1$-bundle over $N$ or the Riemannian cone over $N$ admits a strong Kähler with torsion (SKT) structure. In this way we construct new 6-dimensional SKT manifolds. Moreover, we study the geometric structure induced on …

The paper studies deformations of Calabi-Yau manifolds using Gauduchon metrics.

The abstract discusses conjectures about metrics on complex manifolds.

The paper explores spectral sequences of complex manifolds with special metrics.

We use tools from generalized complex geometry to develop the theory of SKT (a.k.a. pluriclosed Hermitian) manifolds and more generally manifolds with special holonomy with respect to a metric connection with closed skew-symmetric torsion. We develop Hodge theory on such manifolds showing how the reduction of the holon…

We study the existence of three classes of Hermitian metrics on certain types of compact complex manifolds. More precisely, we consider balanced, SKT and astheno-Kähler metrics. We prove that the twistor spaces of compact hyperkähler and negative quaternionic-Kähler manifolds do not admit astheno-Kähler metrics. Then w…

The paper studies non-Kähler LVMB manifolds and their metrics.

The equality between the balanced and the Gauduchon cones is discussed in several situations. In particular, it is shown that equality does not hold on many twistor spaces, and it holds on Moishezon manifolds. Moreover, it is proved that a SKT manifold of dimension three on which the balanced cone equals the Gauduchon …

Study Hermitian metrics with Bismut connection satisfying Bianchi identity and SKT condition.

Study SKT and Kähler structures on specific Lie algebras.

Locally conformal SKT structures are introduced and studied on Lie groups and their compact quotients.

New SKT manifolds created using toric geometry.

In this note we observe that on a 2-step nilpotent Lie group equipped with a left-invariant SKT structure the (1,1)-part of the Bismut-Ricci form is seminegative definite. As application we give a simplified proof of the non-existence of invariant SKT static metrics on 2-step nilmanifolds and of the existence of a long…

Classifies two-step solvable Lie groups with SKT structures.

Study balanced Hermitian structures on almost abelian Lie algebras, classifying six-dimensional cases.

Study of complex structures on specific solvmanifolds, proving existence and non-existence results.

A strong KT (SKT) manifold consists of a Hermitian structure whose torsion three-form is closed. We classify the invariant SKT structures on four-dimensional solvable Lie groups. The classification includes solutions on groups that do not admit compact four-dimensional quotients. It also shows that there are solvable g…

We study the existence of strong Kähler with torsion (SKT) metrics and of symplectic forms taming invariant complex structures $J$ on solvmanifolds $G/Γ$ providing some negative results for some classes of solvmanifolds. In particular, we show that if either $J$ is invariant under the action of a nilpotent complement o…

Study connects Kähler and non-Kähler hyperbolicity.

The paper explores SKT, balanced, and generalized Kähler structures on specific Lie groups.

We prove that any invariant strong Kahler structure with torsion (SKT structure) on a flag manifold M=G/K of a semisimple compact Lie group G is Kahler. As an application we describe invariant generalized Kahler structures on M.

We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex structures. Moreover, in the strong HKT case we construct a metric and three comp…

We give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, an…

A product of Kähler manifolds also carries a Kähler metric. In this short note we would like to study the product of generalized $p-$Kähler manifolds, compact or not. The results we get extend the known results (balanced, SKT, sG manifolds), and are optimal in the compact case. Hence we can give new non-trivial example…

A twist construction for manifolds with torus action is described generalising certain T-duality examples and constructions in hypercomplex geometry. It is applied to complex, SKT, hypercomplex and HKT manifolds to construct compact simply-connected examples. In particular, we find hypercomplex manifolds that admit no …

We review some constructions and properties of complex manifolds admitting pluriclosed and balanced metrics. We prove that for a 6-dimensional solvmanifold endowed with an invariant complex structure J having holomorphically trivial canonical bundle the pluriclosed flow has a long time solution for every invariant init…

Study on properties of Oeljeklaus-Toma manifolds, including cohomology and metrics.

A Hermitian metric $ω$ on a complex manifold is called SKT or pluriclosed if $dd^cω=0$. Let M be a twistor space of a compact, anti-selfdual Riemannian manifold, admitting a pluriclosed Hermitian metric. We prove that in this case M is Kähler, hence isomorphic to $\C P^3$ or a flag space. This result is obtained from r…

We determine the 6-dimensional solvmanifolds admitting an invariant complex structure with holomorphically trivial canonical bundle. Such complex structures are classified up to isomorphism, and the existence of strong Kähler with torsion (SKT), generalized Gauduchon, balanced and strongly Gauduchon metrics is studied.…

This paper classifies LCSKT almost abelian Lie algebras in 6 dimensions.

SKT improves EKI for Bayesian inverse problems with non-Gaussian targets.

Study on special metrics and deformations of solvmanifolds.

We use the procedure of reduction of Courant algebroids to reduce strong KT, hyper KT and generalized Kaehler structures on Courant algebroids. This allows us to recover results from the literature as well as explain from a different angle some of the features observed there in. As an example, we prove that the moduli …

We study evolution of (strong Kähler with torsion) SKT structures via the pluriclosed flow on complex nilmanifolds, i.e. on compact quotients of simply connected nilpotent Lie groups by discrete subgroups endowed with an invariant complex structure. Adapting to our case the techniques introduced by Jorge Lauret for stu…