Lorentz Ricci solitons on 3-dimensional Lie groups

Kensuke Onda

paper

Lorentz Ricci solitons on 3-dimensional Lie groups

arXiv:0906.0086

Abstract

The three-dimensional Heisenberg group $H_{3}$ has three left-invariant Lorentz metrics $g_{1}$ , $g_{2}$ and $g_{3}$ . They are not isometric each other. In this paper, we characterize the left-invariant Lorentzian metric $g_{1}$ as a Lorentz Ricci soliton. This Ricci soliton $g_{1}$ is a shrinking non-gradient Ricci soliton. Likewise we prove that the isometry group of flat Euclid plane E(2) and the isometry group of flat Lorentz plane E(1,1) have Lorentz Ricci solitons.

11 pages, add Section 5, in which we prove that E(1,1) has Lorentz Ricci solitons