Results 11 to 20 of about 174,545 (215)

Conformally Einstein Lorentzian Lie Groups with Heisenberg Symmetry

Results in Mathematics, 2023
We describe all Lorentzian semi-direct extensions of the Heisenberg group which are conformally Einstein. As a by side result, Bach-flat left-invariant Lorentzian metrics on semi-direct extensions of the Heisenberg group are classified, thus providing ...
E. Calviño-Louzao, E. García‐Río, I. Gutiérrez-Rodríguez, R. Vázquez-Lorenzo   +3 more
semanticscholar   +5 more sources

Ricci solitons on four-dimensional Lorentzian Lie groups

Analysis and Mathematical Physics, 2022
We determine all non-Einstein Ricci solitons on four-dimensional Lorentzian Lie groups whose soliton vector field is left-invariant. In addition to pp-wave and plane wave Lie groups, there are four families of Lorentzian metrics on semi-direct extensions
M. Ferreiro-Subrido, E. García‐Río, R. Vázquez-Lorenzo   +2 more
semanticscholar   +4 more sources

Einstein-like Lorentzian Lie groups of dimension four [PDF]

Journal of Nonlinear Mathematical Physics, 2017
Einstein-like examples of four-dimensional Lorentzian Lie groups are listed and geometric properties of each class have been investigated.
A. Zaeim
semanticscholar   +2 more sources

Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups [PDF]

Journal of Geometry and Physics, 2011
We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are sol-solitons. In particular, we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not to be algebraic Ricci solitons.
W. Batat, K. Onda
semanticscholar   +3 more sources

Algebraic Schouten solitons associated to the Bott connection on three-dimensional Lorentzian Lie groups

Electronic Research Archive
In this paper, I define and classify the algebraic Schouten solitons associated with the Bott connection on three-dimensional Lorentzian Lie groups with three different distributions.
Jinguo Jiang
doaj   +2 more sources

Four-dimensional Lorentzian Lie groups

Differential Geometry and its Applications, 2013
The geometric classifications of some classes of four-dimensional simply connected Lie groups with invariant Lorenzian metrics are given. Up to an isomorphism of Lie groups the classification of four-dimensional simply connected Lie groups with invariant Lorenzian metrics is well known.
G. Calvaruso, A. Zaeim
semanticscholar   +3 more sources

Perturbed Bott algebraic Schouten solitons on 3D Lorentzian Lie groups

Electronic Research Archive
In this paper, we defined and classified the algebraic Schouten solitons that are associated with the perturbed Bott connection on three-dimensional Lorentzian Lie groups possessing three distinct distributions.
Xinrui Li, Jiajing Miao, Haiming Liu
doaj   +2 more sources

Conformally Einstein Lorentzian Lie Groups: The Non-solvable Case

Journal of Nonlinear Science
Abstract We describe all left-invariant Bach-flat Lorentz metrics on non-solvable four-dimensional Lie groups, showing that they are conformally Einstein if and only if they are locally conformally flat. As a consequence we show the existence of strictly Bach-flat left-invariant metrics on $$SU(2)\times \mathbb
E. Calviño-Louzao, E. García‐Río, Iván Gutierrez Rodríguez, R. Vázquez-Lorenzo   +3 more
semanticscholar   +4 more sources

(Almost) Ricci Solitons in Lorentzian–Sasakian Hom-Lie Groups

Axioms
We study Lorentzian contact and Lorentzian–Sasakian structures in Hom-Lie algebras. We find that the three-dimensional sl(2,R) and Heisenberg Lie algebras provide examples of such structures, respectively.
Esmaeil Peyghan, Leila Nourmohammadifar, Akram Ali, Ion Mihai   +3 more
doaj   +2 more sources

PARALLEL SURFACES IN THREE-DIMENSIONAL LORENTZIAN LIE GROUPS

Taiwanese Journal of Mathematics, 2010
A three-dimensional homogeneous Lorentzian manifold is either symmetric or locally isometric to a Lie group equipped with a left-invariant Lorentzian metric [4]. We completely classify surfaces with parallel second fundamental form in all non-symmetric homogeneous Lorentzian three-manifolds.
G. Calvaruso, J. Veken
semanticscholar   +4 more sources