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arXiv · 0906.0086

Lorentz Ricci solitons on 3-dimensional Lie groups

Kensuke Onda
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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.

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Kensuke Onda. 2009-07-03. Lorentz Ricci solitons on 3-dimensional Lie groups. https://arxiv.org/abs/0906.0086

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