20 citations · 110 across the 19 of their papers we have counts for
19 papers
Harmful structures and Killing spinors on unimodular Lie groups
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso
A pseudo-Riemannian Einstein manifold with a Killing spinor and Killing constant induces on its nondegenerate hypersurfaces a pair of spinors and a symmetric tensor ,…
Einstein metrics and Killing spinors on pseudo-Riemannian solvmanifolds
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso
Riemannian Einstein solvmanifolds can be described in terms of nilsolitons, namely nilpotent Lie groups endowed with a left-invariant Ricci soliton metric. This characterization do…
A non-Standard Indefinite Einstein Solvmanifold
Federico A. Rossi
We describe an example of an indefinite invariant Einstein metric on a solvmanifold which is not standard, and whose restriction on the nilradical is nondegenerate.
A construction of Einstein solvmanifolds not based on nilsolitons
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso
We construct indefinite Einstein solvmanifolds that are standard, but not of pseudo-Iwasawa type. Thus, the underlying Lie algebras take the form ,…
Pseudo-Kähler and pseudo-Sasaki structures on Einstein solvmanifolds
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso
The aim of this paper is to construct left-invariant Einstein pseudo-Riemannian Sasaki metrics on solvable Lie groups. We consider the class of -standard Sasaki solvab…
Pseudo-Riemannian Sasaki solvmanifolds
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso
We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map rel…
New Special Einstein Pseudo-Riemannian Metrics on Solvable Lie Algebras
Federico A. Rossi
We exhibit a concrete procedure to construct Einstein pseudo-Kähler and para-Kähler metrics on solvable Lie algebras. We apply this method to classify all the rank-one pseudo-Iwasa…
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…
Nice pseudo-Riemannian nilsolitons
Diego Conti, Federico A. Rossi
We study nice nilpotent Lie algebras admitting a diagonal nilsoliton metric. We classify nice Riemannian nilsolitons up to dimension . For general signature, we show that determ…
Indefinite nilsolitons and Einstein solvmanifolds
Diego Conti, Federico A. Rossi
A nilsoliton is a nilpotent Lie algebra with a metric such that , with a derivation. For indefinite metrics, this determ…
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…
Diagram involutions and homogeneous Ricci-flat metrics
Diego Conti, Viviana del Barco, Federico A. Rossi
We introduce a combinatorial method to construct indefinite Ricci-flat metrics on nice nilpotent Lie groups. We prove that every nilpotent Lie group of dimension , every nic…
Ricci-flat and Einstein pseudoriemannian nilmanifolds
Diego Conti, Federico A. Rossi
This is partly an expository paper, where the authors' work on pseudoriemannian Einstein metrics on nilpotent Lie groups is reviewed. A new criterion is given for the existence of…
Indefinite Einstein metrics on nice Lie groups
Diego Conti, Federico A. Rossi
We introduce a systematic method to produce left-invariant, non-Ricci-flat Einstein metrics of indefinite signature on nice nilpotent Lie groups. On a nice nilpotent Lie group, we…
Construction of nice nilpotent Lie groups
Diego Conti, Federico A. Rossi
We illustrate an algorithm to classify nice nilpotent Lie algebras of dimension up to a suitable notion of equivalence; applying the algorithm, we obtain complete listings for…
Einstein nilpotent Lie groups
Diego Conti, Federico A. Rossi
We study the Ricci tensor of left-invariant pseudoriemannian metrics on Lie groups. For an appropriate class of Lie groups that contains nilpotent Lie groups, we introduce a variet…
The Ricci tensor of almost parahermitian manifolds
Diego Conti, Federico A. Rossi
We study the pseudoriemannian geometry of almost parahermitian manifolds, obtaining a formula for the Ricci tensor of the Levi-Civita connection. The formula uses the intrinsic tor…
Degree of non-Kählerianity for 6-dimensional nilmanifolds
Daniele Angella, Maria Giovanna Franzini, Federico Alberto Rossi
We use Bott-Chern cohomology to measure the non-Kählerianity of 6-dimensional nilmanifolds endowed with the invariant complex structures in M. Ceballos, A. Otal, L. Ugarte, and R.…
Cohomology of D-complex manifolds
Daniele Angella, Federico A. Rossi
In order to look for a well-behaved counterpart to Dolbeault cohomology in D-complex geometry, we study the de Rham cohomology of an almost D-complex manifold and its subgroups mad…