Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups
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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. We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are solvsolitons. In particular, we obtain new solitons on $G_{2}$, $G_{5}$, and $G_{6}$, and we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not to be algebraic Ricci solitons.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d0c3c3f23aca61defb3eade0d7c2f11c4057b81a
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In Applied Mathematics
In Astronomy and Astrophysics
In Geometry and Topology
Citations in the corpus
- Examples of Algebraic Ricci Solitons in the Pseudo-Riemannian Case (2011, background): “liton which is not an algebraic Ricci soliton. Indeed, SL(2,R) has left-invariant Lorentzian Ricci solitons (see [3]). But, SL(2,R) does not have an algebraic Ricci soliton which is not Einstein (see [5]). Lauret characterized an algebraic Ricci soliton by some properties in the Riemannian setting. ”