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Lorentz Ricci solitons on 3-dimensional Lie groups

By Kensuke Onda


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.Comment: 11 pages, add Section 5, in which we prove that E(1,1) has Lorentz Ricci soliton

Topics: Mathematics - Differential Geometry, Mathematics - Metric Geometry, 53C15, 53C21, 53C25, 53C30, 53C44, 53C50
Year: 2009
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