Lorentz Ricci Solitons on 3-dimensional Lie groups |
| |
Authors: | Kensuke Onda |
| |
Institution: | 1.Graduate School of Mathematics,Nagoya University,Furocho, Chikusaku,Japan |
| |
Abstract: | 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|