Lorentz Ricci Solitons on 3-dimensional Lie groups

被引：0
作者：
Kensuke Onda
机构：
[1] Nagoya University,Graduate School of Mathematics
来源：
Geometriae Dedicata | 2010年 / 147卷
关键词：
Lie group; Left-invariant Lorentzian metric; Ricci soliton; 53C30; 53C44; 53C50; 22E25;
D O I：
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摘要：
The three-dimensional Heisenberg group H3 has three left-invariant Lorentzian metrics g1, g2, and g3 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 g1 as a Lorentz Ricci Soliton. This Ricci Soliton g1 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.
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页码：313 / 322
页数：9
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