Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups

Details Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups

2011-12-12

arxiv.org/abs/1112.2455v2

Mathematics

Differential Geometry

30 pages

Scientific paper

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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