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Lorentz Ricci Solitons on 3-dimensional Lie groups

2010; Springer Science+Business Media; Volume: 147; Issue: 1 Linguagem: Inglês

10.1007/s10711-009-9456-0

1572-9168

Kensuke Onda,

Geometry and complex manifolds

The three-dimensional Heisenberg group H 3 has three left-invariant Lorentzian metrics g 1, g 2, and g 3 as in Rahmani (J. Geom. Phys. 9(3), 295–302 (1992)). They are not isometric to 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. We also prove that the group E(2) of rigid motions of Euclidean 2-space and the group E(1, 1) of rigid motions of Minkowski 2-space have Lorentz Ricci Solitons.