Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups

Abstract

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.

30 pages

References in corpus (2)

• Lorentz Ricci solitons on 3-dimensional Lie groups
• Three-dimensional Lorentzian homogeneous Ricci solitons

Cited by in corpus (4)

• Nilsolitons of H-type in the Lorentzian setting
• On the moduli spaces of left-invariant pseudo-Riemannian metrics on Lie groups
• Conformally flat pseudo Riemannian Homogeneous Ricci Solitons 4 spaces
• Examples of algebraic Ricci solitons in the Pseudo-Riemannian case