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Papers by Sergio Garbiero

The Backlund problem for the equation f(x,t)z_xx - z_tt=0

A characterizartion of locally 3-symmetric spaces

A characterizartion of locally 3-symmetric spaces

The Backlund problem for the equation f(x,t)z_xx - z_tt=0

Misura di Haar su Gruppi Topologici

We establish the existence of solvable Lie groups of dimension 4 and leftinvariant Riemannian met... more We establish the existence of solvable Lie groups of dimension 4 and leftinvariant Riemannian metrics with zero Bach tensor which are neither conformally Einstein nor half conformally flat.

Esercizi di Algebra Lineare e Geometria Analitica

We establish the existence of solvable Lie groups of dimension 4 and leftinvariant Riemannian met... more We establish the existence of solvable Lie groups of dimension 4 and leftinvariant Riemannian metrics with zero Bach tensor which are neither conformally Einstein nor half conformally flat.

Almost Hermitian geometry of 6-dimensional nilmanifolds

Complementi DI Matematica Gruppi e Rappresentazioni

A characterization of locally 3-symmetric spaces

Three-dimensional P-spaces of constant scalar curvature

Rendiconti del Seminario Matematico

On some types of almost Hermitian homogeneous structures

Comparing the classifications of almost Hermitian structures and almost Hermitian homogeneous str... more Comparing the classifications of almost Hermitian structures and almost Hermitian homogeneous structures, we obtain some geometrical results about different classes of almost Hermitian homogeneous manifolds. In particular we study the Lie groups endowed with left invariant metrics and compatible almost complex structures. Some examples are discussed in detail.

Einstein metrics on some special manifolds

Arxiv preprint math/0007066, 2000

The fundamental 2-form of an invariant almost Hermitian structure on a 6-dimensional Lie group is... more The fundamental 2-form of an invariant almost Hermitian structure on a 6-dimensional Lie group is described in terms of an action by SO(4)×U(1) on complex projective 3-space. This leads to a combinatorial description of the classes of almost Hermitian structures on the Iwasawa and other nilmanifolds.

Proceedings of the Edinburgh Mathematical Society, 1988

Let (M, g, J) be an almost Hermitian manifold. More precisely, M is a ∞ differentiable manifold o... more Let (M, g, J) be an almost Hermitian manifold. More precisely, M is a ∞ differentiable manifold of dimension 2n, J is an almost complex structure on M, i.e. it is a tensor field of type (1, 1) such thatfor any X∈(M), ((M) is the Lie algebra of ∞ vector fields on M), and g is a Riemannian metric compatible with J, i.e.

Comptes Rendus Mathematique, 2013

We establish the existence of solvable Lie groups of dimension 4 and left-invariant Riemannian me... more We establish the existence of solvable Lie groups of dimension 4 and left-invariant Riemannian metrics with zero Bach tensor which are neither conformally Einstein nor half conformally flat.

Hermitian geometry on the Iwasawa manifold

The Backlund problem for the equation f(x,t)z_xx - z_tt=0

A characterizartion of locally 3-symmetric spaces

A characterizartion of locally 3-symmetric spaces

The Backlund problem for the equation f(x,t)z_xx - z_tt=0

Misura di Haar su Gruppi Topologici

We establish the existence of solvable Lie groups of dimension 4 and leftinvariant Riemannian met... more We establish the existence of solvable Lie groups of dimension 4 and leftinvariant Riemannian metrics with zero Bach tensor which are neither conformally Einstein nor half conformally flat.

Esercizi di Algebra Lineare e Geometria Analitica

We establish the existence of solvable Lie groups of dimension 4 and leftinvariant Riemannian met... more We establish the existence of solvable Lie groups of dimension 4 and leftinvariant Riemannian metrics with zero Bach tensor which are neither conformally Einstein nor half conformally flat.

Almost Hermitian geometry of 6-dimensional nilmanifolds

Complementi DI Matematica Gruppi e Rappresentazioni

A characterization of locally 3-symmetric spaces

Three-dimensional P-spaces of constant scalar curvature

Rendiconti del Seminario Matematico

On some types of almost Hermitian homogeneous structures

Comparing the classifications of almost Hermitian structures and almost Hermitian homogeneous str... more Comparing the classifications of almost Hermitian structures and almost Hermitian homogeneous structures, we obtain some geometrical results about different classes of almost Hermitian homogeneous manifolds. In particular we study the Lie groups endowed with left invariant metrics and compatible almost complex structures. Some examples are discussed in detail.

Einstein metrics on some special manifolds

Arxiv preprint math/0007066, 2000

The fundamental 2-form of an invariant almost Hermitian structure on a 6-dimensional Lie group is... more The fundamental 2-form of an invariant almost Hermitian structure on a 6-dimensional Lie group is described in terms of an action by SO(4)×U(1) on complex projective 3-space. This leads to a combinatorial description of the classes of almost Hermitian structures on the Iwasawa and other nilmanifolds.

Proceedings of the Edinburgh Mathematical Society, 1988

Let (M, g, J) be an almost Hermitian manifold. More precisely, M is a ∞ differentiable manifold o... more Let (M, g, J) be an almost Hermitian manifold. More precisely, M is a ∞ differentiable manifold of dimension 2n, J is an almost complex structure on M, i.e. it is a tensor field of type (1, 1) such thatfor any X∈(M), ((M) is the Lie algebra of ∞ vector fields on M), and g is a Riemannian metric compatible with J, i.e.

Comptes Rendus Mathematique, 2013

We establish the existence of solvable Lie groups of dimension 4 and left-invariant Riemannian me... more We establish the existence of solvable Lie groups of dimension 4 and left-invariant Riemannian metrics with zero Bach tensor which are neither conformally Einstein nor half conformally flat.

Hermitian geometry on the Iwasawa manifold