Florida International University

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19922026

most citedThe Gaia mission

7.1k citations

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math.DG2024

On the existence of balanced metrics of Hodge-Riemann type

Anna Fino, Asia Mainenti

In the paper we study the existence of balanced metrics of Hodge-Riemann type on non-Kähler complex manifolds. We first find some general obstructions, for instance that a Hodge-Ri…

math.DG2024★ 5 cited

CYT and SKT manifolds with parallel Bismut torsion

Beatrice Brienza, Anna Fino, Gueo Grantcharov

In the present paper, we study compact complex manifolds admitting a Hermitian metric which is SKT and CYT and whose Bismut torsion is parallel. We first obtain a characterization…

math.DG2023★ 1 cited

A note on $p$ -Kähler structures on compact quotients of Lie groups

Anna Fino, Asia Mainenti

A $p$ -Kähler structure on a complex manifold of complex dimension $n$ is given by a $d$ -closed transverse real $(p, p)$ -form. In the paper we study the existence of $p$ -Kähler struc…

math.DG2023

On the existence of homogeneous solitons of gradient type for the G $_{2}$ -Laplacian flow

Anna Fino, Alberto Raffero

In this note, we prove the existence of homogeneous gradient solitons for the G $_{2}$ -Laplacian flow by providing the first known example of this type. This result singles out the G$…

math.DG2022★ 1 cited

CYT and SKT Metrics on Compact Semi-Simple Lie Groups

Anna Fino, Gueo Grantcharov

A Hermitian metric on a complex manifold $(M, I)$ of complex dimension $n$ is called Calabi-Yau with torsion (CYT) or Bismut-Ricci flat, if the restricted holonomy of the associate…

math.DG2022

Special Hermitian structures on suspensions

Anna Fino, Gueo Grantcharov, Misha Verbitsky

Motivated by the construction based on topological suspension of a family of compact non-Kähler complex manifolds with trivial canonical bundle given by L. Qin and B. Wang in [QW],…

math.DG2021★ 2 cited

Exact G $_{2}$ -structures on compact quotients of Lie groups

Anna Fino, Lucía Martín-Merchán, Alberto Raffero

We show that the compact quotient $Γ\ G$ of a seven-dimensional simply connected Lie group $G$ by a co-compact discrete subgroup $Γ \subset G$ does…

math.DG2021★ 3 cited

Almost Robinson geometries

Anna Fino, Thomas Leistner, Arman Taghavi-Chabert

We investigate the geometry of almost Robinson manifolds, Lorentzian analogues of almost Hermitian manifolds, defined by Nurowski and Trautman as Lorentzian manifolds of even dimen…

math.DG2016★ 13 cited

Quasi-asymptotically conical Calabi-Yau manifolds

Ronan J. Conlon, Anda Degeratu, Frédéric Rochon

We construct new examples of quasi-asymptotically conical (QAC) Calabi-Yau manifolds that are not quasi-asymptotically locally Euclidean (QALE). We do so by first providing a natur…

math.DG2016★ 6 cited

Algebraic dimension of complex nilmanifolds

Anna Fino, Gueo Grantcharov, Misha Verbitsky

Let M be a complex nilmanifold, that is, a compact quotient of a nilpotent Lie group endowed with an invariant complex structure by a discrete lattice. A holomorphic differential o…

math.DG2015

A note on tame/compatible almost complex structures on four-dimensional Lie algebras

Andres Cubas, Tedi Draghici

Four-dimensional, oriented Lie algebras $g$ which satisfy the tame-compatible question of Donaldson for all almost complex structures $J$ on $g$ are completel…

math.DG2014

Poisson structures on twistor spaces of hyperkaehler and HKT manifolds

Gueo Grantcharov, Lisandra Hernandez-Vazquez

We characterize HKT structure in terms of nondegenrate complex Poisson bivector on hypercomplex manifold. We extend the characterization to the twistor space. After considering the…

math.DG2014★ 17 cited

Existence of HKT metrics on hypercomplex manifolds of real dimension 8

Gueo Grantcharov, Mehdi Lejmi, Misha Verbitsky

A hypercomplex manifold $M$ is a manifold equipped with three complex structures satisfying quaternionic relations. Such a manifold admits a canonical torsion-free connection prese…

math.DG2014★ 11 cited

The SO(3) monopole cobordism and superconformal simple type

Paul M. N. Feehan, Thomas G. Leness

We show that the SO(3) monopole cobordism formula from Feehan and Leness (2002) implies that all smooth, closed, oriented four-manifolds with $b^{1} = 0$ and $b^{+} \geq 3$ and odd with S…

math.DG2014★ 11 cited

Superconformal simple type and Witten's conjecture

Paul M. N. Feehan, Thomas G. Leness

Let $X$ be a smooth, closed, connected, orientable four-manifold with $b^{1} (X) = 0$ and $b^{+} (X) \geq 3$ and odd. We show that if $X$ has Seiberg-Witten simple type, then the SO(3)-mono…

math.DG2012★ 11 cited

Compact complex surfaces with geometric structures related to split quaternions

Johann Davidov, Gueo Grantcharov, Oleg Mushkarov +1

We study the problem of existence of geometric structures on compact complex surfaces that are related to split quaternions. These structures, called para-hypercomplex, para-hyperh…

math.DG2009★ 5 cited

Generalized pseudo Kaehler structures

J. Davidov, G. Grantcharov, O. Muskarov +1

In the paper we consider pseudo bihermitian structures - a pair of complex structures compatible with a pseudo Riemannian metric. As in the positive definite case we establish its…

math.DG2008★ 1 cited

Degeneracy loci of families of Dirac operators

Thomas G. Leness

Generalizing some results from R. Leung's thesis, we compute, in rational cohomology, the Poincare dual of the degeneracy locus of the family of Dirac operators parameterized by th…

math.DG2006★ 6 cited

Witten's conjecture for many four-manifolds of simple type

Paul M. N. Feehan, Thomas G. Leness

We prove that Witten's Conjecture [arXiv:hep-th/9411102] on the relationship between the Donaldson and Seiberg-Witten series for a four-manifold of Seiberg-Witten simple type with…

math.DG2003★ 13 cited

The odd-dimensional Goldberg Conjecture

Vestislav Apostolov, Tedi Draghici, Andrei Moroianu

An odd-dimensional version of the Goldberg conjecture was formulated and proved by Boyer and Galicki, using an orbifold analogue of Sekigawa's formulas, and an approximation argume…

math.DG2003★ 3 cited

Calabi-Yau Connections with Torsion on Toric Bundles

D. Grantcharov, G. Grantcharov, Y. S. Poon

We find sufficient conditions for a principal toric bundle over compact Kähler manifolds to admit Calabi-Yau connections with torsion. With the aids of a topological classification…

math.DG2002★ 27 cited

An SO(3)-monopole cobordism formula relating Donaldson and Seiberg-Witten invariants

Paul M. N. Feehan, Thomas G. Leness

We prove an analogue of the Kotschick-Morgan conjecture in the context of SO(3) monopoles, obtaining a formula relating the Donaldson and Seiberg-Witten invariants of smooth four-m…

math.DG2001

Local models and integrability of certain almost Kahler 4-manifolds

Vestislav Apostolov, John Armstrong, Tedi Draghici

We classify, up to a local isometry, all non-Kahler almost Kahler 4-manifolds for which the fundamental 2-form is an eigenform of the Weyl tensor, and whose Ricci tensor is invaria…

math.DG2001★ 22 cited

SO(3) Monopoles, Level-One Seiberg-Witten Moduli Spaces, and Witten's Conjecture in Low Degrees

Paul M. N. Feehan, Thomas G. Leness

We prove Witten's formula relating the Donaldson and Seiberg-Witten series modulo powers of degree $c + 2$ , with $c = - 1/4 (7 χ + 11 σ)$ , for four-manifolds obeying some mild conditions,…

On the existence of balanced metrics of Hodge-Riemann type

CYT and SKT manifolds with parallel Bismut torsion

A note on p-Kähler structures on compact quotients of Lie groups

On the existence of homogeneous solitons of gradient type for the G2​-Laplacian flow

CYT and SKT Metrics on Compact Semi-Simple Lie Groups

Special Hermitian structures on suspensions

Exact G2​-structures on compact quotients of Lie groups

Almost Robinson geometries

Quasi-asymptotically conical Calabi-Yau manifolds

Algebraic dimension of complex nilmanifolds

A note on tame/compatible almost complex structures on four-dimensional Lie algebras

Poisson structures on twistor spaces of hyperkaehler and HKT manifolds

Existence of HKT metrics on hypercomplex manifolds of real dimension 8

The SO(3) monopole cobordism and superconformal simple type

Superconformal simple type and Witten's conjecture

Compact complex surfaces with geometric structures related to split quaternions

Generalized pseudo Kaehler structures

Degeneracy loci of families of Dirac operators

Witten's conjecture for many four-manifolds of simple type

The odd-dimensional Goldberg Conjecture

Calabi-Yau Connections with Torsion on Toric Bundles

An SO(3)-monopole cobordism formula relating Donaldson and Seiberg-Witten invariants

Local models and integrability of certain almost Kahler 4-manifolds

SO(3) Monopoles, Level-One Seiberg-Witten Moduli Spaces, and Witten's Conjecture in Low Degrees

A note on $p$ -Kähler structures on compact quotients of Lie groups

On the existence of homogeneous solitons of gradient type for the G $_{2}$ -Laplacian flow

Exact G $_{2}$ -structures on compact quotients of Lie groups