Lorentz Ricci solitons on 3-dimensional Lie groups

2009/06/01 by Onda, Kensuke · 1 citation
#53C15 #53C21 #53C25 #53C30 #53C44 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.0906.0086

Abstract

The three-dimensional Heisenberg group H₃ has three left-invariant Lorentz metrics g₁, g₂ and g₃. They are not isometric each other. In this paper, we characterize the left-invariant Lorentzian metric g₁ as a Lorentz Ricci soliton. This Ricci soliton g₁ 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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