8 citations · 53 across the 17 of their papers we have counts for
21 papers
Weyl-Einstein structures on conformal solvmanifolds
Viviana del Barco, Andrei Moroianu, Arthur Schichl
A conformal Lie group is a conformal manifold such that has a Lie group structure and is the conformal structure defined by a left-invariant metric on . We s…
Ad-invariant metrics on nonnice nilpotent Lie algebras
Diego Conti, Viviana del Barco, Federico A. Rossi
We proved in previous work that all real nilpotent Lie algebras of dimension up to carrying an ad-invariant metric are nice. In this paper we show by constructing explicit exa…
Uniqueness of ad-invariant metrics
Diego Conti, Viviana del Barco, Federico A. Rossi
We consider Lie algebras admitting an ad-invariant metric, and we study the problem of uniqueness of the ad-invariant metric up to automorphisms. This is a common feature in low di…
Conformal Killing forms on -step nilpotent Riemannian Lie groups
Viviana del Barco, Andrei Moroianu
We study left-invariant conformal Killing - or -forms on simply connected -step nilpotent Riemannian Lie groups. We show that if the center of the group is of dimension gr…
Conformal Killing symmetric tensors on Lie groups
Viviana del Barco, Andrei Moroianu
We introduce the notion of metric Lie algebras of Killing type, which are characterized by the fact that all conformal Killing symmetric tensors are sums of Killing tensors and mul…
Purely coclosed G-structures on 2-step nilpotent Lie groups
Viviana del Barco, Andrei Moroianu, Alberto Raffero
We consider left-invariant (purely) coclosed G-structures on 7-dimensional 2-step nilpotent Lie groups. According to the dimension of the commutator subgroup, we obtain various…
Higher degree Killing forms on step nilmanifolds
Viviana del Barco, Andrei Moroianu
We study left-invariant Killing forms of arbitrary degree on simply connected step nilpotent Lie groups endowed with left-invariant Riemannian metrics, and classify them when t…
Killing forms on -step nilmanifolds
Viviana del Barco, Andrei Moroianu
We study left-invariant Killing -forms on simply connected -step nilpotent Lie groups endowed with a left-invariant Riemannian metric. For , we show that every left-in…
Symmetric Killing tensors on nilmanifolds
Viviana del Barco, Andrei Moroianu
We study left-invariant symmetric Killing 2-tensors on 2-step nilpotent Lie groups endowed with a left-invariant Riemannian metric, and construct genuine examples, which are not li…
On generalized -structures and -duality
Viviana del Barco, Lino Grama
This is a short note on generalized -structures obtained as a consequence of a -dual construction given in a previous work of the authors together with Leonardo Soriani. Gi…
-duality on nilmanifolds
Viviana del Barco, Lino Grama, Leonardo Soriani
We study generalized complex structures and -duality (in the sense of Bouwknegt, Evslin, Hannabuss and Mathai) on Lie algebras and construct the corresponding Cavalcanti and Gua…
Lie algebras admitting symmetric, invariant and nondegenerate bilinear forms
Viviana del Barco
We present structural properties of Lie algebras admitting symmetric, invariant and nondegenerate bilinear forms. We show that these properties are not satisfied by nilradicals of…
Nilradicals of parabolic subalgebras admitting symplectic structures
Leandro Cagliero, Viviana del Barco
In this paper we describe all the nilradicals of parabolic subalgebras of split real simple Lie algebras admitting symplectic structures. The main tools used to obtain this list ar…
Homogeneous geodesics in pseudo-Riemannian nilmanifolds
Viviana del Barco
We study the geodesic orbit property for nilpotent Lie groups when endowed with a pseudo-Riemannian left-invariant metric. We consider this property with respect to different g…
Lorentzian compact manifolds: isometries and geodesics
V. del Barco, G. P. Ovando, F. Vittone
In this work we investigate families of compact Lorentzian manifolds in dimension four. We show that every lightlike geodesic on such spaces is periodic, while there are closed and…
Isometric actions on pseudo-Riemannian nilmanifolds
Viviana del Barco, Gabriela P. Ovando
This work deals with the structure of the isometry group of pseudo-Riemannian 2-step nilmanifolds. We study the action by isometries of several groups and we construct examples sho…
Naturally reductive pseudo-Riemannian Lie groups in low dimensions
Viviana del Barco, Gabriela P. Ovando, Francisco Vittone
This work concerns the non-flat metrics on the Heisenberg Lie group of dimension three $\Heis_3(\RR)$ and the bi-invariant metrics on the solvable Lie groups of dimension four. On…
Symplectic structures on nilmanifolds: an obstruction for its existence
Viviana J. del Barco
In this work we introduce an obstruction for the existence of symplectic structures on nilpotent Lie algebras. Indeed, a necessary condition is presented in terms of the cohomology…
On a spectral sequence for the cohomology of a nilpotent Lie algebra
Viviana J. del Barco
Given a nilpotent Lie algebra we construct a spectral sequence which is derived from a filtration of its Chevalley-Eilenberg differential complex and converges to the…
Symplectic Structures on Free Nilpotent Lie algebras
Viviana del Barco
In this work we study the problem of existence of symplectic structures on free nilpotent Lie algebras. Necessary and sufficient conditions are given for even dimensional ones. The…
Free Nilpotent Lie Algebras Admitting Ad-Invariant Metrics
Gabriela Ovando, Viviana del Barco
In this work we find necessary and sufficient conditions for a free nilpotent or a free metabelian nilpotent Lie algebra to be endowed with an ad-invariant metric. For such nilpote…