arXiv subjects

Francesca Salvatore

Publications and source records attributed to Francesca Salvatore.

3 recordsLinked to original sources

arXiv2025

On the existence of balanced metrics on six-manifolds of cohomogeneity one

We consider balanced metrics on complex manifolds with holomorphically trivial canonical bundle, most commonly known as balanced $\rm{SU}(n)$-structures. Such structures are of interest for both Hermitian geometry and string theory, since they provide the ideal setting for the Hull-Strominger system. In this paper, we provide a non-existence result for balanced non-Kähler $\rm{SU}(3)$-structures which are invariant under a cohomogeneity one action on simply connected six-manifolds.

math.DG↗

arXiv2021

Closed G$_2$-structures on unimodular Lie algebras with non-trivial center

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 algebras with non-trivial center admitting closed G$_2$-structures, up to isomorphism, and we show that six of them arise as the contactization of a symplectic Lie algebra. Finally, we prove that every semi-algebraic soliton on the contactization of a symplectic Lie algebra must be expanding, and we determine all unimodular Lie algebras with center of dimension at least two that admit semi-algebraic solitons, up to isomorphism.

math.DG↗

arXiv2021

Closed $\text{SL}(3,\mathbb{C})$-structures on nilmanifolds

In this paper we consider closed $\text{SL}(3,\mathbb{C})$-structures which are either mean convex or tamed by a symplectic form. These notions were introduced by Donaldson in relation to $\text{G}_2$-manifolds with boundary. In particular, we classify nilmanifolds which carry an invariant mean convex closed $\text{SL}(3,\mathbb{C})$-structure and those which admit an invariant mean convex half-flat $\text{SU}(3)$-structure. We also prove that, if a solvmanifold admits an invariant tamed closed $\text{SL}(3,\mathbb{C})$-structure, then it also has an invariant symplectic half-flat $\text{SU}(3)$-structure.

math.DG↗