13 citations · 27 across the 14 of their papers we have counts for
18 papers · 1 filter
Complex symplectic structures: deformations and cohomology
Giovanni Bazzoni, Marco Freibert, Adela Latorre +1
We show that complex symplectic structures need not be preserved under small deformations, and we find sufficient conditions for this to happen. We study various cohomologies of co…
Torsion-free -structures on almost Abelian solvmanifolds
Marco Freibert
In this article, we provide a general set-up for arbitrary linear Lie groups which allows to characterise the almost Abelian Lie algebras admittin…
Generalised Einstein metrics on Lie groups
Vicente Cortés, Marco Freibert, Mateo Galdeano
We continue the systematic study of left-invariant generalised Einstein metrics on Lie groups initiated in arXiv:2206.01157. Our approach is based on a new reformulation of the cor…
Complex Symplectic Lie Algebras with Large Abelian Subalgebras
Giovanni Bazzoni, Marco Freibert, Adela Latorre +1
We present two constructions of complex symplectic structures on Lie algebras with large abelian ideals. In particular, we completely classify complex symplectic structures on almo…
Compatibility of balanced and SKT metrics on two-step solvable Lie groups
Marco Freibert, Andrew Swann
It has been conjectured by Fino and Vezzoni that a compact complex manifold admitting both a compatible SKT and a compatible balanced metric also admits a compatible Kähler metric.…
Closed -eigenforms and exact -structures
Marco Freibert, Simon Salamon
A study is made of left-invariant -structures with an exact 3-form on a Lie group whose Lie algebra admits a codimension-one nilpotent ideal $\math…
Two-step solvable SKT shears
Marco Freibert, Andrew Swann
We use the shear construction to construct and classify a wide range of two-step solvable Lie groups admitting a left-invariant SKT structure. We reduce this to a specification of…
A non Ricci-flat Einstein pseudo-Riemannian metric on a 7-dimensional nilmanifold
Marisa Fernández, Marco Freibert, Jonatan Sánchez
We answer in the affirmative the question posed by Conti and Rossi on the existence of nilpotent Lie algebras of dimension 7 with an Einstein pseudo-metric of nonzero scalar curvat…
Homogeneous spinor flow
Marco Freibert, Lothar Schiemanowski, Hartmut Weiss
We study the spinor flow on homogeneous spin manifolds. After providing the general setup we discuss the homogeneous spinor flow in dimension 3 and on almost abelian Lie groups in…
The shear construction
Marco Freibert, Andrew Swann
The twist construction is a method to build new interesting examples of geometric structures with torus symmetry from well-known ones. In fact it can be used to construct arbitrary…
SU(4)-holonomy via the left-invariant hypo and Hitchin flow
Marco Freibert
The Hitchin flow constructs eight-dimensional Riemannian manifolds (M,g) with holonomy in Spin(7) starting with a cocalibrated G_2-structure on a seven-dimensional manifold. As Sp(…
Solvable groups and a shear construction
Marco Freibert, Andrew Swann
The twist construction is a geometric model of T-duality that includes constructions of nilmanifolds from tori. This paper shows how one-dimensional foliations on manifolds may be…
On the boundary behaviour of left-invariant Hitchin and hypo flows
Florin Belgun, Vicente Cortés, Marco Freibert +1
We investigate left-invariant Hitchin and hypo flows on -, - and -dimensional Lie groups. They provide Riemannian cohomogeneity-one manifolds of one dimension higher with…
Calibrated and parallel structures on almost Abelian Lie algebras
Marco Freibert
In this article, we determine the seven-dimensional almost Abelian Lie algebras which admit calibrated or parallel G_2-/G_2^*-structures. Along the way, we show that certain well-e…
Cocalibrated G_2-structures on products of four- and three-dimensional Lie groups
Marco Freibert
Cocalibrated G_2-structures are structures naturally induced on hypersurfaces in Spin(7)-manifolds. Conversely, one may start with a seven-dimensional manifold M endowed with a coc…
Half-flat structures on indecomposable Lie groups
Marco Freibert, Fabian Schulte-Hengesbach
This article can be viewed as a continuation of the articles arXiv:0912.3486 and arXiv:1012.3714 where the decomposable Lie algebras admitting half-flat SU(3)-structures are classi…
Cocalibrated structures on Lie algebras with a codimension one Abelian ideal
Marco Freibert
Cocalibrated G_2-structures and cocalibrated G_2^*-structures are the natural initial values for Hitchin's evolution equations whose solutions define (pseudo)-Riemannian manifolds…
Half-flat structures on decomposable Lie groups
Marco Freibert, Fabian Schulte-Hengesbach
Half-flat SU(3)-structures are the natural initial values for Hitchin's evolution equations whose solutions define parallel G_2-structures. Together with the results of arXiv:0912.…