16 citations · 87 across the 25 of their papers we have counts for
18 papers · 1 filter
Purely coclosed -structures on nilmanifolds -- II
Giovanni Bazzoni, Giorgia Petracci
This paper completes the classification of seven-dimensional nilpotent Lie groups endowed with a left-invariant purely coclosed -structure, initiated by the first-named…
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…
Moduli spaces of (co)closed -structures on nilmanifolds
Giovanni Bazzoni, Alejandro Gil-García
We compute the dimensions of some moduli spaces of left-invariant closed and coclosed -structures on 7-dimensional nilmanifolds, showing that they are not related to…
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…
Symmetric and skew-symmetric complex structures
Giovanni Bazzoni, Alejandro Gil-García, Adela Latorre
On a complex manifold , we interpret complex symplectic and pseudo-Kähler structures as symplectic forms with respect to which is, respectively, symmetric and skew-symme…
Spin-harmonic structures and nilmanifolds
Giovanni Bazzoni, Lucia Martin-Merchan, Vicente Munoz
We introduce spin-harmonic structures, a class of geometric structures on Riemannian manifolds of low dimension which are defined by a harmonic unitary spinor. Such structures are…
Special types of locally conformal closed G-structures
Giovanni Bazzoni, Alberto Raffero
Motivated by analogous results in locally conformal symplectic geometry, we study different classes of G-structures defined by a locally conformal closed 3-form. In particular,…
Toric actions in cosymplectic geometry
Giovanni Bazzoni, Oliver Goertsches
We show that compact toric cosymplectic manifolds are mapping tori of equivariant symplectomorphisms of toric symplectic manifolds.
Locally conformally symplectic and Kähler geometry
Giovanni Bazzoni
The goal of this note is to give an introduction to locally conformally symplectic and Kähler geometry. In particular, Sections 1 and 3 aim to provide the reader with enough mathem…
Structure of locally conformally symplectic Lie algebras and solvmanifolds
Daniele Angella, Giovanni Bazzoni, Maurizio Parton
We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct lo…
Parallel forms, co-Kähler Manifolds and their Models
Giovanni Bazzoni, Gregory Lupton, John Oprea
We show how certain topological properties of co-Kähler manifolds derive from those of the Kähler manifolds which construct them. In particular, we show that the existence of paral…
Vaisman nilmanifolds
Giovanni Bazzoni
We prove that if a compact nilmanifold is endowed with a Vaisman structure, then is isomorphic to the Cartesian product of the Heisenberg group with $\mathbb{R}…
Homotopic properties of Kähler orbifolds
Giovanni Bazzoni, Indranil Biswas, Marisa Fernández +2
We prove the formality and the evenness of odd-degree Betti numbers for compact Kähler orbifolds, by adapting the classical proofs for Kähler manifolds. As a consequence, we obtain…
A splitting theorem for compact Vaisman manifolds
Giovanni Bazzoni, Juan Carlos Marrero, John Oprea
We extend to metric compact mapping tori a splitting result for coKähler manifolds. In particular, we prove that a compact Vaisman manifold is finitely covered by the product of a…
On locally conformal symplectic manifolds of the first kind
Giovanni Bazzoni, Juan Carlos Marrero
We present some examples of locally conformal symplectic structures of the first kind on compact nilmanifolds which do not admit Vaisman metrics. One of these examples does not adm…
Locally conformal symplectic nilmanifolds with no locally conformal Kähler metrics
Giovanni Bazzoni, Juan Carlos Marrero
We obtain an example of a compact locally conformal symplectic nilmanifold which admits no locally conformal Kähler metrics. This gives a new positive answer to a question raised b…
K-cosymplectic manifolds
Giovanni Bazzoni, Oliver Goertsches
In this paper we study K-cosymplectic manifolds, i.e., smooth cosymplectic manifolds for which the Reeb field is Killing with respect to some Riemannian metric. These structures ge…
On the structure of co-Kähler manifolds
Giovanni Bazzoni, John Oprea
By the work of Li, a compact co-Kähler manifold is a mapping torus , where is a Kähler manifold and is a Hermitian isometry. We show here that there is always a fi…