Alberto Raffero

activity

20132026

most citedOn the automorphism group of a closed G

_{2}

-structure

17 citations · 125 across the 31 of their papers we have counts for

collaborators

32 papers

math.DG2026

Complete pluriclosed metrics with vanishing Bismut Ricci form on the affine quadric

Fabio Podestà, Alberto Raffero

We study a one-parameter family of SO(4)-invariant pluriclosed Hermitian metrics $g_{c}$ with vanishing Bismut Ricci form on the affine quadric $Q_{3} ≅ T S^{3}$ , previously described…

math.DG2025

The heterotic G $_{2}$ -system on 2-step nilmanifolds endowed with principal torus bundles

Andrei Moroianu, Alberto Raffero, Luigi Vezzoni

We study the geometric heterotic G $_{2}$ -system on 7-dimensional 2-step nilmanifolds $M = Γ\ N$ endowed with principal torus bundles and with a prescribed flat tangent bundle…

math.DG2025

Pluripotential theory and special holonomy, I: Hodge decompositions and $\partial \partial ˉ$ lemmata

Tommaso Pacini, Alberto Raffero

Let $M$ be a compact torsion-free $G_{2}$ 7-manifold or Calabi-Yau 6-manifold. We prove Hodge decomposition theorems for the $d d^{ϕ}$ operators, introduced by Harvey and Lawson, which…

math.DG2024★ 3 cited

Three-dimensional positively curved generalized Ricci solitons with SO(3)-symmetries

Fabio Podestà, Alberto Raffero

We prove the existence of a one-parameter family of pairwise non-isometric, complete, positively curved, steady generalized Ricci solitons of gradient type on $R^{3}$ that a…

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.DG2023★ 7 cited

The twisted G $_{2}$ equation for strong G $_{2}$ -structures with torsion

Anna Fino, Lucía Martín-Merchán, Alberto Raffero

We discuss general properties of strong G $_{2}$ -structures with torsion and we investigate the twisted G $_{2}$ equation, which represents the G $_{2}$ -analogue of the twisted Calabi-Yau e…

math.DG2022

Variation formulae for the volume of coassociative submanifolds

Tommaso Pacini, Alberto Raffero

We prove new variation formulae for the volume of coassociative submanifolds, expressed in terms of $G_{2}$ data. As a special case, we obtain a second variation formula for variatio…

math.DG2022★ 8 cited

Infinite families of homogeneous Bismut Ricci flat manifolds

Fabio Podestà, Alberto Raffero

Starting from compact symmetric spaces of inner type, we provide infinite families of compact homogeneous spaces carrying invariant non-flat Bismut connections with vanishing Ricci…

math.DG2022

Bismut Ricci flat manifolds with symmetries

Fabio Podestà, Alberto Raffero

We construct examples of compact homogeneous Riemannian manifolds admitting an invariant Bismut connection that is Ricci flat and non-flat, proving in this way that the generalized…

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★ 1 cited

Special solutions to the Type IIA flow

Alberto Raffero

We consider the source-free Type IIA flow introduced by Fei-Phong-Picard-Zhang, and we study it in the case where the relevant geometric datum is a symplectic half-flat SU(3)-struc…

math.DG2021

Closed G $_{2}$ -structures on unimodular Lie algebras with non-trivial center

Anna Fino, Alberto Raffero, Francesca Salvatore

We characterize the structure of a seven-dimensional Lie algebra with non-trivial center endowed with a closed G $_{2}$ -structure. Using this result, we classify all unimodular Lie al…

math.DG2020★ 3 cited

On the dynamical behaviour of the generalized Ricci flow

Alberto Raffero, Luigi Vezzoni

Motivated by Müller-Haslhofer results on the dynamical stability and instability of Ricci-flat metrics under the Ricci flow, we obtain dynamical stability and instability results f…

math.DG2020★ 5 cited

Purely coclosed G $_{2}$ -structures on 2-step nilpotent Lie groups

Viviana del Barco, Andrei Moroianu, Alberto Raffero

We consider left-invariant (purely) coclosed G $_{2}$ -structures on 7-dimensional 2-step nilpotent Lie groups. According to the dimension of the commutator subgroup, we obtain various…

math.DG2020

Recent results on closed G $_{2}$ -structures

Anna Fino, Alberto Raffero

We review recent results concerning closed G $_{2}$ -structures on seven-dimensional manifolds. In particular, we discuss the construction of examples and some related problems.

math.DG2019

Closed G $_{2}$ -structures with a transitive reductive group of automorphisms

Fabio Podestà, Alberto Raffero

We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G $_{2}$ -structure and admitting a transitive reductive group G of automorphis…

math.DG2019★ 6 cited

Remarks on homogeneous solitons of the G $_{2}$ -Laplacian flow

Anna Fino, Alberto Raffero

We show the existence of expanding solitons of the G $_{2}$ -Laplacian flow on non-solvable Lie groups, and we give the first example of a steady soliton that is not an extremally Ricc…

math.DG2019★ 5 cited

Exact $G_{2}$ -structures on unimodular Lie algebras

Marisa Fernández, Anna Fino, Alberto Raffero

We consider seven-dimensional unimodular Lie algebras $g$ admitting exact $G_{2}$ -structures, focusing our attention on those with vanishing third Betti number $b_3(\mathf…

math.DG2019★ 2 cited

Homogeneous 8-manifolds admitting invariant Spin(7)-structures

Dmitri Alekseevsky, Ioannis Chrysikos, Anna Fino +1

We study compact, simply connected, homogeneous 8-manifolds admitting invariant Spin(7)-structures, classifying all canonical presentations G/H of such spaces, with G simply connec…

math.DG2018★ 1 cited

Special types of locally conformal closed G $_{2}$ -structures

Giovanni Bazzoni, Alberto Raffero

Motivated by analogous results in locally conformal symplectic geometry, we study different classes of G $_{2}$ -structures defined by a locally conformal closed 3-form. In particular,…

math.DG2018★ 1 cited

On $G_{2}$ -structures, special metrics and related flows

Marisa Fernández, Anna Fino, Alberto Raffero

We review results about $G_{2}$ -structures in relation to the existence of special metrics, such as Einstein metrics and Ricci solitons, and the evolution under the Laplacian flow on…

math.DG2018★ 10 cited

A class of eternal solutions to the G $_{2}$ -Laplacian flow

Anna Fino, Alberto Raffero

We explicitly describe the solution of the G $_{2}$ -Laplacian flow starting from an extremally Ricci-pinched closed G $_{2}$ -structure on a compact 7-manifold and we investigate its prop…

math.DG2018★ 3 cited

On the automorphism group of a symplectic half-flat 6-manifold

Fabio Podestà, Alberto Raffero

We prove that the automorphism group of a compact 6-manifold $M$ endowed with a symplectic half-flat SU(3)-structure has abelian Lie algebra with dimension bounded by min$\{5,b_1(M…

math.DG2018★ 17 cited

On the automorphism group of a closed G $_{2}$ -structure

Fabio Podestà, Alberto Raffero

We study the automorphism group of a compact 7-manifold $M$ endowed with a closed non-parallel G $_{2}$ -structure, showing that its identity component is abelian with dimension bounde…

Complete pluriclosed metrics with vanishing Bismut Ricci form on the affine quadric

The heterotic G2​-system on 2-step nilmanifolds endowed with principal torus bundles

Pluripotential theory and special holonomy, I: Hodge decompositions and ∂∂ˉ lemmata

Three-dimensional positively curved generalized Ricci solitons with SO(3)-symmetries

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

The twisted G2​ equation for strong G2​-structures with torsion

Variation formulae for the volume of coassociative submanifolds

Infinite families of homogeneous Bismut Ricci flat manifolds

Bismut Ricci flat manifolds with symmetries

Exact G2​-structures on compact quotients of Lie groups

Special solutions to the Type IIA flow

Closed G2​-structures on unimodular Lie algebras with non-trivial center

On the dynamical behaviour of the generalized Ricci flow

Purely coclosed G2​-structures on 2-step nilpotent Lie groups

Recent results on closed G2​-structures

Closed G2​-structures with a transitive reductive group of automorphisms

Remarks on homogeneous solitons of the G2​-Laplacian flow

Exact G2​-structures on unimodular Lie algebras

Homogeneous 8-manifolds admitting invariant Spin(7)-structures

Special types of locally conformal closed G2​-structures

On G2​-structures, special metrics and related flows

A class of eternal solutions to the G2​-Laplacian flow

On the automorphism group of a symplectic half-flat 6-manifold

On the automorphism group of a closed G2​-structure

The heterotic G $_{2}$ -system on 2-step nilmanifolds endowed with principal torus bundles

Pluripotential theory and special holonomy, I: Hodge decompositions and $\partial \partial ˉ$ lemmata

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

The twisted G $_{2}$ equation for strong G $_{2}$ -structures with torsion

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

Closed G $_{2}$ -structures on unimodular Lie algebras with non-trivial center

Purely coclosed G $_{2}$ -structures on 2-step nilpotent Lie groups

Recent results on closed G $_{2}$ -structures

Closed G $_{2}$ -structures with a transitive reductive group of automorphisms

Remarks on homogeneous solitons of the G $_{2}$ -Laplacian flow

Exact $G_{2}$ -structures on unimodular Lie algebras

Special types of locally conformal closed G $_{2}$ -structures

On $G_{2}$ -structures, special metrics and related flows

A class of eternal solutions to the G $_{2}$ -Laplacian flow

On the automorphism group of a closed G $_{2}$ -structure