Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups

Wafaa Batat; Kensuke Onda

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arXiv · 1112.2455

Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups

Wafaa Batat·Kensuke Onda

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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.

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Wafaa Batat, Kensuke Onda. 2012-04-01. Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. https://arxiv.org/abs/1112.2455

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